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International audience; We have derived a new Young’s formula for the polarization-averaged molecular frame photoelectron angular distributions (PA-MFPADs), as a bond length ruler for dissociating hetero-diatomic molecules. The relative errors against numerical results were within 5 %. © 2022 The Author(s).

In this article, we report a critical assessment of dielectric function calculations in electron gas through the comparison of different modelling methods. This work is motivated by the fact that the dielectric function is a key quantity in the multiple scattering description of plasmon features in various electron-based spectroscopies. Starting from the standard random phase approximation (RPA) expression, we move on to correlation-augmented RPA, then damped RPA models. Finally, we study the reconstruction of the dielectric function from its moments, using the Nevanlinna and memory function approaches. We find the memory function method to be the most effective, being highly flexible and customizable., 14 pages, 9 figures

International audience; A number of renormalization schemes for improving the convergence of multiple scattering series expansions are investigated. Numerical tests on a small Cu(111) cluster demonstrate their effectiveness, for example increasing the rate of convergence by up to a factor 2 or by transforming a divergent series into a convergent one. These techniques can greatly facilitate multiple scattering calculations, especially for spectroscopies such as photoelectron diffraction, Auger electron diffraction, low energy electron diffraction , where an electron propagates with a kinetic energy of hundreds of eV in a cluster of hundreds of atoms.

The structural, electronic and elastic properties of full- Heusler alloys Co2CrZ (Z=Si,Al) and their quaternary compound Co2CrSi1-xAlx, are determined using the full potential linearized augmented plane waves (FP- LAPW) method based on (GGA) the Generalized Gradient Approximation and density functional theory (DFT) implemented in the WIEN2k package. As results, quaternary compound in CuHg2Ti-type crystal structure are stable. Density of states (DOS) and bands structure show the existence of energies band gaps in their minority-spin channels with half-metallic behavior. The lattice constant of new quaternary alloys Co2CrSi1-xAlx exhibits a small deviation from Vegard's law and a marginal deviation of the bulk modulus from linear concentration. The three independent elastic constants (C11, C12, and C44) are calculated from the direct computation of the stresses generated by small strains. Besides, we report the variation of the elastic constants as a function of pressure as well. From the calculated elastic constants, the mechanical character of Co2CrSi1-xAlx is predicted; elastic constants are calculated to investigate stability criteria and the mechanical nature of the studied materials. The quaternary compound is found to be mechanically anisotropic, ductile and meet the elastic stability criteria. A regular solution model is used to investigate the thermodynamic stability of the alloy which essentially shows a miscibility gap phase by calculating the critical temperatures of the alloys.

We present a theoretical study of the polarization-averaged molecular-frame photoelectron angular distributions (PA-MFPADs) emitted from the 1s orbital of oxygen atoms of dissociating dicationic carbon monoxide CO2+. Due to the polarization average, the contribution of the direct wave of the photoelectron, which represents the largest contribution to the MFPADs, is removed, so that the PA-MFPADs clearly show the details of the scattering image of the photoelectron. As a result, it is necessary to employ an accurate theory for the theoretical analysis of the continuum state. In this study, we apply a full-potential multiple scattering theory, where the space is partitioned into Voronoi polyhedra and truncated spheres, to take into account the electron charge density outside the physical atomic spheres. We do not use the spherical harmonic expansion of the cell shape functions to avoid divergence problems. The potentials in the scattering cells are computed using the multiconfigurational second-order perturbation theory restricted active space method to take into account the influence of the core hole in the electron charge density in the final state, so that a realistic relaxation can be achieved. We show that the full-potential treatment plays an important role in the PA-MFPADs at a photoelectron kinetic energy of 100 eV. In contrast, the PA-MFPADs are not sensitive to any type of major excited states in the Auger final state. We also study the dynamics of the CO2+ dissociation. We find that the PA-MFPADs dramatically change their shape as a function of the C–O bond length.

International audience; A brief derivation of the cross section in the independent particle approximation for some of the spectroscopies treated in the msspec program package is presented. We solve the related Schrödinger equation with a complex energy-dependent effective potential in the framework of multiple scattering theory to write the cross-section for photoemission and photoabsorption in a physically transparent way that provides insight in their interpretation and analysis. Relativistic corrections are also implemented. In order to be able to apply this theory to a wide variety of systems we use a kind of all-purpose optical potential, depending only on the local density of the system under investigation, and discuss its merits and drawbacks. A Green’s function approach is shown to be necessary to write the photoabsorption cross section in the case of complex potential. © 2018, Springer International Publishing AG, part of Springer Nature.

International audience; In this introductory chapter, we develop the scattering theory necessary to understand the theoretical models underlying the multiple scattering codes. First, the elementary theory is presented and it is then formalized to introduce the different operators whose matrix elements are computed in the codes. Then, we extend the theory to the case of a collection of potentials, i.e. multiple scattering. Finally we outline the way cross-sections can be derived from the multiple scattering framework and give some practical examples. © 2018, Springer International Publishing AG, part of Springer Nature.

International audience; We derive a general spherical wave multiple scattering expression of the EELS cross-section. Contrarily to most of the previous theoretical frameworks, this approach treats all the electrons involved on an equal footing with respect to multiple scattering. The main point in our results is that the cross-section depends not only on Coulomb integrals on the absorbing atom, but also on contributions from all the other atoms. We show that these external contributions should be restricted to neighbouring atoms. © 2018, Springer International Publishing AG, part of Springer Nature.

International audience; Ballistic Electron Emission Microscope (BEEM) is a microscope to investigate Schottky barrier based on Scanning Tunneling Microscope (STM) setup. The theoretical scheme widely used for STM is mostly focusing on an electric current from the tip tunneling through the vacuum to the sample surface. However, this model is not applicable for BEEM, since in the BEEM case, electrons tunneling through the vacuum are transported in the material over a very long range. We propose a theoretical model based on the real space full potential multiple scattering theory in order to describe this transport phenomena within the one electron picture. It is analogous to the theoretical model of angle resolved photoemission, except that the electron is emitted from the tip. This framework describes the tunneling effect and the multiple scattering in the tip and the sample and between them. Moreover this theory can be applied for non-Hermitian Hamiltonian, so that the loss of electrons at the Schottky barrier can be mimicked by introducing an imaginary part in the optical potential. © 2018, Springer International Publishing AG, part of Springer Nature.

International audience; We present a scattering theoretic approach to the calculation of the cross-section of (e,2e) impact spectroscopy where all the electrons involved are treated within the real space multiple scattering framework. This approach is particularly suited to the reflection geometry at low kinetic energies, with the ejection of a core-level electron. In this case, we expect (e,2e) spectroscopy can be turned into an extremely sensitive surface structure probe. © 2018, Springer International Publishing AG, part of Springer Nature.

International audience; X-ray Photoelectron Spectroscopy (XPS) used in quantitative chemical analysis of solid surfaces requires subtraction of a broad background, arising from various energy loss mechanisms, to obtain reliable core level peak intensities. Besides single electron excitation, collective electron oscillations (plasmons) can be excited in the bulk and at the surface. Photoelectron energy loss spectroscopy (XPS-PEELS) is a non-destructive tool useful for both process control and thin film metrology. This review emphasizes its versatility to elucidate material research issues. The energy loss function (ELF) is useful for thin film growth optimization since it gives insight in valence electron density, hardness, optical band gap and interface properties such as adhesion and wetting. XPS-PEELS also provides depth and width of implanted atom profiles in solid targets, e.g. Ar nanobubbles in Al. Special emphasis is given to the retrieval of electronic properties from XPS-PEELS data. Since the ELF, < Im[-1/(q, )] >q, is related to the q-averaged dielectric function, q, the latter can be obtained by taking into account multiple bulk and surface plasmon excitations. This task is rather simple in wide band gap materials where the ELF and the no-loss peak are clearly separated, as illustrated by amorphous silicon, amorphous carbon or Al oxide data. In contrast, in metals or small band gap materials, the broad asymmetric photoemission peak overlaps the ELF and low energy features in the ELF may be lost. A Fourier Transform (FT) method is proposed to analyze PEELS data, with the objective of retrieving such low energy excitations, e.g. inter band transitions. This FT method is compared with an empirical method based on a smooth cutoff of the zero-loss peak, using PEELS data obtained from Al2O3. Current developments of a quantum mechanical theory are crucial to obtain the respective contributions of intrinsic and extrinsic plasmon excitation (along with their interference) and to assess some approximations performed in classical treatments.

We propose a comparative and critical assessment of multiple scattering expansions. The so-called multiple scattering series expansion is much used in the description of spectroscopies at higher energies. However, it is plagued with convergence problems when operated at lower energies. We compare this method to related methods that can be found in the literature, relying both on finite and infinite expansions. After discussing the pros and cons of these methods, we establish a simple alternative to multiple scattering series expansion which has a wider and faster range of convergence. [DOI: 10.1380/ejssnt.2012.599]

Some important phonon effects observed in X-ray absorption and X-ray photoemission spectra are discussed on the basis of nonequilibrium Green's function theory. This theoretical framework allows us to incorporate phonon effects, such as Debye–Waller (DW) factors, Franck–Condon (FC) factors and electron–phonon interactions in a natural way. In the case of core level excitations, we can take into account the core–hole effects in lesser Green's function g and photoelectron propagation in greater Green's function g > . For the core–hole propagation we derive some formulas to describe the thermally displaced core functions: we have p components even for deep core s orbital due to the thermal motion. We should notice that the thermal fluctuation is quite small but it is already in the order of the spread of the core functions. Applying Mermin's theorem, we can calculate the thermal average of the hole propagator g : here an important ingredient is the Debye–Waller factor used in X-ray and neutron diffraction. For the pre-edge structures, the intensity associated with forbidden electric dipole transition is sensitive to the temperature compared with allowed electric quadrupole transition. We also discuss the FC and their interference, which have negligible contribution to pre-edge intensity and energy shift. The quasi-particle energy is also influenced by the core displacement which can be responsible for the peak shift of the pre-edges. We also discuss the changes of the photoelectron angular distributions caused by the thermal atomic vibration.

We derive here a general, basis-independent, multiple scattering theory in a partitioned space. For this, we decompose a given set of atoms into non-intersecting subsets and construct the multiple scattering theory associated with these objects. We show that all the actual theories of electron spectroscopies are particular cases of our theory but that many other choices can be made to give a more adequate description of these spectroscopies. In that way, this theory is highly customizable to the problem under study.

We propose here a systematic and straightforward way to include point-group symmetries into the theory of photoelectron diffraction. In addition to reducing the number of scattering path operators that have to be calculated, this approach permits as well as to derive a new algorithm to minimize the number of paths that have to be explored in the series expansion cluster method by making use of path degeneracies.

This paper presents a general theory of electron energy loss spectroscopy based on a recently developed basis-independent multiple-scattering formalism. This approach allows to establish the cross-section in a physically transparent way. An application to the particular case of spherical waves in a real space representation is made to show the flexibility of the method.

We describe a Full Multiple Scattering (MS) code for the calculation of photoelectron diffraction (PD) patterns from solid surfaces. The use of a complex potential allows the calculation of complex phase shifts which describe realistically the damping of the electronic wave during its path to the detector. Full convergence in the scattering path expansion due to the inversion of the multiple scattering matrix makes this method particularly reliable in the surface sensitive energy range of the photoelectron, where approximate solutions in terms of series expansion and/or real potential calculations lead to inaccuracies in the determination of structural parameters. In this form the code is suitable to applications to clean surfaces such as Surface Core Level Shift Photoelectron Diffraction (SCLS-PD).

Gaunt coefficients, the integrated products of three spherical harmonics, are widely used in several branches of physics. Here, I review the most recent methods to calculate them efficiently (i.e. with an extensive use of their symmetry properties) and propose a new one which is faster and remarkably stable in terms of accuracy in the range of energies generally encountered in electron spectroscopies.

By combining x-ray excited Auger electron diffraction experiments and multiple scattering calculations we reveal a layer-resolved shift for the Mg $K{L}_{23}{L}_{23}$ Auger transition in MgO ultrathin films (4--6 \AA{}) on Ag(001). This resolution is exploited to demonstrate the possibility of controlling Mg atom incorporation at the $\mathrm{MgO}/\mathrm{Ag}(001)$ interface by exposing the MgO films to a Mg flux. A substantial reduction of the $\mathrm{MgO}/\mathrm{Ag}(001)$ work function is observed during the exposition phase and reflects both band-offset variations at the interface and band bending effects in the oxide film.

In some cases, high energy photoelectron diffraction peaks corresponding to well defined crystallographic directions show a splitting that cannot be explained by the traditional interpretation. Such an effect occurs in the O 1s 0° peak in MgO(001). Using cluster calculations, we demonstrate that this effect is induced by close neighbours via an inter-chain process and explain why it does not occur for the Mg 2s peak.

International audience; Methodological advances in multiple scattering theory (MST) in both wave and Green's function versions are reported for the calculation of electronic ground and excited state properties of condensed matter systems with an emphasis on core-level photoemission and absorption spectra. Full-potential MST is reviewed and extended to non-local potentials. Multichannel MST is reformulated in terms of the multichannel density matrix whereby strong electron correlation of atomic multiplet type can be accounted for in both ground and excited states.

Angle-resolved X-ray photoelectron spectroscopy (XPS) has been used to characterise chemically etched GaAs(001) versus epitaxially grown surfaces. The measured amplitude of X-ray photoelectron diffraction (XPD) modulation is then an excellent probe of the local structural environment around the emitter atom in the near-surface substrate. The observed modulations are here compared to the results of single- and double-scattering cluster calculations with a fine agreement. Moreover, because of our choice of the emission plane and taking into account the similarity in the scattering factors of Ga and As atoms, XPD effects can be almost eliminated from the angular variation of the fractional peak ratio IAs(IAs + IGa) which is then easily related to the arsenic concentration profile CAs(z). A best-fitting procedure is used to select the experimental concentration depth profile which characterises the surface under study. Samples exposed to different technological treatments, like ion implantation, chemical etching and annealing have been studied and compared. The concentrations of As atoms at the surface for As-capped, MBE-grown (001) samples after annealing around 350°C and for chemically etched GaAs(001) wafers indicate the same type of surface (As-terminated) as far as composition and structure are concerned.

We have studied the growth and magnetic properties of thin Fe-Ge films synthesized (codeposited at room temperature and postannealed at $250\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}$) on Ge(111) wafers versus stoichiometry. Morphology and crystal structure have been investigated in situ by means of scanning tunneling microscopy, low-energy electron diffraction, and x-ray photoelectron diffraction and ex situ with x-ray diffraction. The magnetic properties were characterized ex situ by conventional polar and longitudinal magneto-optical Kerr effect and transverse biased initial inverse susceptibility and torque measurements. It is found that the growth is epitaxial for Ge content up to $\ensuremath{\sim}48\text{ }\text{at}\text{.}\text{ }\mathrm{%}$ ($\ensuremath{\sim}{\text{Fe}}_{1.1}\text{Ge}$ composition). In particular, the film is homogeneous and flat and adopts a crystalline structure of hexagonal symmetry derived from the $\text{B}{8}_{2}$ $({\text{Ni}}_{2}\text{In})$ structure over a wide stoichiometry range extending from ${\text{Fe}}_{2}\text{Ge}$ to ${\text{Fe}}_{1.1}\text{Ge}$. The epitaxial orientation between the Ge substrate and the germanide layer is $(0001)\text{Fe-Ge}\ensuremath{\parallel}(111)\text{Ge}$ with $[11\overline{2}0]\text{Fe-Ge}\ensuremath{\parallel}[\overline{1}10]\text{Ge}$. We found however that the surface periodicity and the out-of-plane lattice parameter $c$ evolve within this stoichiometry range and two distinct stoichiometry regimes appear on both sides of a critical stoichiometry $(\ensuremath{\sim}{\text{Fe}}_{1.5}\text{Ge})$. Indeed, from ${\text{Fe}}_{2}\text{Ge}$ to ${\text{Fe}}_{1.5}\text{Ge}$ the surface periodicity is $p(2\ifmmode\times\else\texttimes\fi{}2)$ and $c$ continuously decreases with Fe content, whereas from ${\text{Fe}}_{1.5}\text{Ge}$ to ${\text{Fe}}_{1.1}\text{Ge}$ the surface periodicity is $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})R30\ifmmode^\circ\else\textdegree\fi{}$ and $c$ remains constant. These features have been interpreted as a clear fingerprint of a minor transformation of the crystalline structure but without any change in symmetry. This structural order transformation is discussed in relation to previous results reported in the case of macroscopic single-crystal Fe-Ge ingots. On both sides of the wide $[{\text{Fe}}_{2}\text{Ge},{\text{Fe}}_{1.1}\text{Ge}]$ composition range the layer is no more homogeneous. More precisely, for higher Fe content the film contains both the above mentioned ${\text{Ni}}_{2}\text{In}$-derived phase and a Fe-richer phase (probably bcc Fe) whereas for higher Ge content the layer is amorphous. Magnetic characterization showed in particular that the homogeneous ${\text{Ni}}_{2}\text{In}$-derived epilayers are ferromagnetic with a Curie temperature that varies drastically with the stoichiometry, rising up to a high ${T}_{\text{C}}$ value of $\ensuremath{\sim}450\text{ }\text{K}$ for the Fe-rich ${\text{Fe}}_{1.9}\text{Ge}$ composition. Finally, whatever the stoichiometry, the magnetic easy axis of the homogeneous phase lies in the film plane and a small uniaxial anisotropy is superimposed on a sixfold order one that results from the hexagonal symmetry of the crystallographic structure.

International audience; We introduce a powerful alternative expansion method to perform multiple scattering calculations. In contrast to standard MS series expansion, where the scattering contributions are grouped in terms of scattering order and may diverge in the low energy region, this expansion, called correlation expansion, partitions the scattering process into contributions from different small atom groups and converges at all energies. It converges faster than MS series expansion when the latter is convergent. Furthermore, it takes less memory than the full MS method so it can be used in the near edge region without any divergence problem, even for large clusters. The correlation expansion framework we derive here is very general and can serve to calculate all the elements of the scattering path operator matrix. Photoelectron diffraction calculations in a cluster containing 23 atoms are presented to test the method and compare it to full MS and standard MS series expansion.

International audience; We have developed a generalization of the multiple-scattering formalism to deal with Auger-photoelectron coincidence spectroscopy APECS in the solid state. We have merged the exact atomic treatment of the angular correlations between the two electrons and the single-particle approach, on which the multiplescattering description of condensed matter relies. This allows the recovering, even in extended systems, of the entangled form of the electron-pair wave function characterizing the coincidence angular diffraction pattern. In the atomic limit our formalism correctly reproduces the cross section, as calculated within the statistical-tensors approach, usually employed in atomic physics. We have then performed numerical calculations for the Ge100 L3M45M45 APECS and compared the results with previous experiments. We found that, in the given geometry, the diffraction patterns in coincidence with different directions of the photoelectron keep little memory of the atomic anisotropy. We speculate on the conditions to be fulfilled in order to enhance the atomic-orbital sensitivity in APECS through solid-state diffraction effects.

International audience; In this paper we present a single-particle scattering approach for the angular correlation between a photoelectron and the subsequent Auger electron from atomic targets. This method is proposed as an alternative approach with respect to the usual density matrix formalism, since it is more convenient for extension to the solid state case. Such an extension is required by the great progress made in the field of coincidence spectroscopy in condensed matter systems. We derived a tensor expression for the cross section and an equivalent expression in terms of convenient angular functions has been treated for the case of linearly polarized light. Numerical calculations are performed for the L3M2,3M2,3 transition in argon, in the single configuration Dirac-Fock scheme. Results are compared with experimental data for different final angular momentum states of the doubly charged ion and for different kinematical conditions.

We give a basic introduction to the physical phenomena underlying x-ray and electron spectroscopies. We review as well all the side effects, such as manybody ones, that can affect the spectra measured experimentally. Some ele- ments of multiple-scattering theory are given to formulate a description of these techniques. Finally, in the particular case of the determination of structural para- meters, a tentative methodology is outlined.

International audience; We present a unitary cluster approach to the calculation of several electron and photon spectroscopies, ranging from core and valence level photoelectron diffraction and absorption to electron, Auger and anomalous diffraction. Electron energy loss and Auger-photoelectron coincidence spectroscopies can also be treated in the same frame. This approach is based on multiple-scattering theory with a complex optical potential of the Hedin-Lundqvist type and is valid for all electron kinetic energies. Similarities and differences between these diffraction techniques are examined and cluster size convergence is discussed in connection with the electron mean free path. Applications to selected problems are presented to illustrate the method, both for structural and electronic analysis.

The properties of MgO/Ag(001) ultrathin films with substitutional Mg atoms in the interface metal layer have been investigated by means of Auger electron diffraction experiments, ultraviolet photoemission spectroscopy, and density functional theory (DFT) calculations. Exploiting the layer-by-layer resolution of the Mg KL_23 L_23 Auger spectra and using multiple scattering calculations, we first determine the interlayer distances as well as the morphological parameters of the MgO/Ag(001) system with and without Mg atoms incorporated at the interface. We find that the Mg atoms incorporation drives a strong distortion of the interface layers and that its impact on the metal/oxide electronic structure is an important reduction of the work function (0.5 eV) related to band-offset variations at the interface. These experimental observations are in very good agreement with our DFT calculations which reproduce the induced lattice distortion and which reveal (through a Bader analysis) that the increase of the interface Mg concentration results in an electron transfer from Mg to Ag atoms of the metallic interface layer. Although the local lattice distortion appears as a consequence of the attractive (repulsive) Coulomb interaction between O2- ions of the MgO interface layer and the nearest positively (negatively) charged Mg (Ag) neighbors of the metallic interface layer, its effect on the work function reduction is only limited. Finally, an analysis of the induced work function changes in terms of charge transfer, rumpling, and electrostatic compression contributions is attempted and reveals that the metal/oxide work function changes induced by interface Mg atoms incorporation are essentially driven by the increase of the electrostatic compression effect., 13 pages, 8 figures

We establish chemical-shift low-energy photoelectron diffraction as a novel and powerful method for the determination of clean surface structures. Combined with a new theoretical approach based on full multiple scattering theory with complex potential, the method is applied to the case of the InP(110) clean surface relaxation. The extreme sensitivity of this technique to structural parameters allows us to measure with good accuracy both the first layer and the second layer relaxation angle (respectively 23\ifmmode^\circ\else\textdegree\fi{} and -5\ifmmode^\circ\else\textdegree\fi{}).

International audience; We explore the convergence of the multiple scattering series by studying the spectral radius of the corresponding multiple scattering matrix. The energy variations of this spectral radius exhibit strong oscillations. These oscillations are shown to depend strongly on the electronic and crystallographic structure in the low energy regime. As the calculation of the eigenvalues of the multiple scattering matrix is very long, we devise a fast algorithm to approximate this spectral radius.

International audience; Black phosphorus (BPh) is a layered material with strong in-plane anisotropy of its structural and electronic properties; in spite of the great potential of BPh for conceptually new devices in optoelectronics and plasmonics, its fundamental electronic excitations have not yet been fully elucidated. In order to discriminate collective (plasmons) and single-particle (inter band transitions) excitations, we investigate the energy-loss distribution of P 1s photoelectrons in hard X-ray photoelectron spectra of BPh over a wide energy range. The energy-loss function (ELF), averaged over the principal directions of the BPh crystal, has been retrieved by using a Fourier Transform analysis to eliminate multiple inelastic scattering events. At low loss energies (1-8 eV), weak unresolved energy loss peaks are well described by DFT calculated inter band transitions, showing some anisotropy in the dielectric function ε(ω,q) tensor of BPh. At high loss energies, the ELF is dominated by the collective excitation of valence electrons with a peak energy at 20.1±0.2 eV, and weak anisotropy is found in the DFT calculated Im(-1/ε) tensor. The anomalously small peak energy (9.0±0.5 eV) of a weak surface plasmon resonance is attributed either to low surface electron density in the terminal phosphorene layer or to some anisotropic surface plasmon propagation.