Final State Contributions Research Articles

Chemical significance of x-ray photoelectron spectroscopy binding energy shifts: A Perspective

The principal intent of this Perspective is to review the mechanisms that are responsible for the shifts of binding energies, ΔBE, observed in x-ray photoelectron spectroscopy (XPS) measurements and so to relate the shifts to the electronic structure and the chemical bonding in the systems studied. To achieve this goal, several theoretical considerations are necessary beyond just the calculation of XPS BEs. Though briefly discussed here, we are not primarily interested in absolute values of BE or quantitation using relative intensities. Within the molecular orbital (MO) theory framework, it is shown that the analysis of orbital properties is critical for the correct interpretation of XPS. In particular, rigorous definitions are given for the initial state and final state contributions to BEs and to BE shifts, ΔBE. It is first shown how the BEs of core levels are related to the electronic structure by consideration of the BEs for a model atomic system to establish the origins and magnitudes of BE shifts. The mechanisms established for the model system are then applied to a review of XPS measurements and MO theory on a set of real examples. An important focus of the paper is to demonstrate that, in many cases, initial state mechanisms allow for a definitive interpretation of the XPS BE shifts and that an important role of theory is to provide qualitative explanations rather than quantitative agreement with XPS measurements. The mechanisms established are a guide to the interpretation of XPS measurements and consideration of these mechanisms may suggest additional calculations that would be useful. It is concluded that there is still a bright future for the coupling of ab initio MO theory with XPS measurements.

Effect of electron correlation in the decomposition of core level binding energy shifts into initial and final state contributions.

The influence of electron correlation into the decomposition of core level binding energy shifts, measured by X-ray photoelectron spectroscopy (XPS), into initial and final effects is analysed for a series of molecules where these effects are noticeable. Moreover, the series of molecules is chosen in such a way that electron delocalization and increasing number of electrons may provide a large screening of the core hole. A detailed analysis shows that the Hartree-Fock decomposition is biased whereas a physically meaningful decomposition is obtained when electron correlation effects are taken into account. The results show that in this case, trends in core level binding energy shifts are driven by initial state effects thus providing further support to the use of these observable quantities to interpret changes in the chemical bond in the neutral molecule rather than on the core ionized cation. Consequences for the theoretical interpretation of XPS data in materials and surface science are discussed.

Electronic structure of FeO, γ−Fe2O3 , and Fe3O4 epitaxial films using high-energy spectroscopies

We study the electronic structure of well-characterized epitaxial films of FeO (wustite), $\ensuremath{\gamma}\ensuremath{-}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ (maghemite), and ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ (magnetite) using hard x-ray photoelectron spectroscopy (HAXPES), x-ray absorption near-edge spectroscopy (XANES), and electron energy loss spectroscopy (EELS). We carry out HAXPES with incident photon energies of 12 and 15 keV in order to probe the bulk-sensitive Fe $1s$ and Fe $2p$ core level spectra. Fe $K$-edge XANES is used to characterize and confirm the Fe valence states of FeO, $\ensuremath{\gamma}\ensuremath{-}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$, and ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ films. EELS is used to identify the bulk plasmon loss features. A comparison of HAXPES results with model calculations for an $M{\mathrm{O}}_{6}$ cluster provides us with microscopic electronic structure parameters such as the onsite Coulomb energy ${U}_{dd}$, the charge-transfer energy $\mathrm{\ensuremath{\Delta}}$, and the metal-ligand hybridization strength $V$. The results also provide estimates for the ground-state and final-state contributions in terms of the ${d}^{n}, {d}^{n+1}{\underline{L}}^{1}$, and ${d}^{n+2}{\underline{L}}^{2}$ configurations. Both FeO and $\ensuremath{\gamma}\ensuremath{-}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ can be described as charge-transfer insulators in the Zaanen-Sawatzky-Allen picture with ${U}_{dd}\phantom{\rule{4pt}{0ex}}>\phantom{\rule{4pt}{0ex}}\mathrm{\ensuremath{\Delta}}$, consistent with earlier work. However, the $M{\mathrm{O}}_{6}$ cluster calculations do not reproduce an extra satellite observed in Fe $1s$ spectra of $\ensuremath{\gamma}\ensuremath{-}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ and ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$. Based on simplified calculations using an ${M}_{2}{\mathrm{O}}_{7}$ cluster with renormalized parameters, it is suggested that nonlocal screening plays an important role in explaining the two satellites observed in the Fe $1s$ core level HAXPES spectra of $\ensuremath{\gamma}\ensuremath{-}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ and ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$.

Top quark pair production at NNLO in the quark-antiquark channel

We present the derivation of the NNLO two-parton final state contributions to top pair production in the quark-antiquark channel proportionnal to the leading colour factor $N_c^2$. Together with the three and four-parton NNLO contributions presented in a previous publication, this enables us to complete the phenomenologically most important NNLO corrections to top pair hadro-production in this channel. We derive this two-parton contribution using the massive extension of the NNLO antenna subtraction formalism and implement those corrections in a parton-level event generator providing full kinematical information on all final state particles. In addition, we also derive the heavy quark contributions proportional to $N_h$. Combining the new leading-colour and heavy quark contributions together with the light quark contributions derived previously, we present NNLO differential distributions for LHC and Tevatron. We also compute the differential top quark forward-backward asymmetry at Tevatron and find that our results are in good agreement with the measurements by the D0 collaboration.

Prediction of core level binding energies in density functional theory: Rigorous definition of initial and final state contributions and implications on the physical meaning of Kohn-Sham energies.

A systematic study of the N(1s) core level binding energies (BE's) in a broad series of molecules is presented employing Hartree-Fock (HF) and the B3LYP, PBE0, and LC-BPBE density functional theory (DFT) based methods with a near HF basis set. The results show that all these methods give reasonably accurate BE's with B3LYP being slightly better than HF but with both PBE0 and LCBPBE being poorer than HF. A rigorous and general decomposition of core level binding energy values into initial and final state contributions to the BE's is proposed that can be used within either HF or DFT methods. The results show that Koopmans' theorem does not hold for the Kohn-Sham eigenvalues. Consequently, Kohn-Sham orbital energies of core orbitals do not provide estimates of the initial state contribution to core level BE's; hence, they cannot be used to decompose initial and final state contributions to BE's. However, when the initial state contribution to DFT BE's is properly defined, the decompositions of initial and final state contributions given by DFT, with several different functionals, are very similar to those obtained with HF. Furthermore, it is shown that the differences of Kohn-Sham orbital energies taken with respect to a common reference do follow the trend of the properly calculated initial state contributions. These conclusions are especially important for condensed phase systems where our results validate the use of band structure calculations to determine initial state contributions to BE shifts.

Initial and Final State Effects in the Ultraviolet and X-ray Photoelectron Spectroscopy (UPS and XPS) of Size-Selected Pdn Clusters Supported on TiO2(110)

Photoelectron spectroscopy is a powerful tool for investigating the electronic structure of supported clusters, especially when initial state and final state contributions to the electron binding energy can be separated. We have performed a combined experimental and theoretical study of ultraviolet and X-ray photoelectron spectroscopy (UPS and XPS) using atomically size-selected Pdn clusters on rutile TiO2(110). Theoretical investigations allow for the UPS and XPS shifts to be split into initial state and final state contributions. In XPS, the occupation of the 4d orbital of Pd controls the initial state shift offering information about the hybridization of the cluster, while the size and the charging of the cluster controls the final state shift. In UPS, we evaluate two methods for calculating the final state shift in periodic unit cells and find that both methods give reasonable results for pristine TiO2; however, using a p-type dopant fails when two separate donor–acceptor pairs are present. The observed UPS shifts can be described by combining the surface dipole and the final state shifts. Metallic contacts to the semiconductor surface result in band alignment between the metallic contact and the cluster, shifting the Fermi level to lie just below the conduction band of the TiO2. Information about the charge state and hybridization of the cluster are revealed by separating the initial and final state effects.

The Wagner plot and the Auger parameter as tools to separate initial- and final-state contributions in X-ray photoemission spectroscopy

The application of the Wagner plot and Auger parameter concepts as tools for the identification of chemical states of atoms in molecules or solids is growing steadily in the surface science literature. In several publications, however, the chemical and physical insights provided by such conceptual tools are not fully investigated. In this contribution it is shown how easy is to use the Wagner plot to get information on the local valence charge and Madelung (molecular) potential (initial-state effects) and on the extra-atomic relaxation energy gained from the environment (final-state effects) for a core-ionized atom. To cover the gap with previous reviews on the applications of the Wagner plot and the Auger parameter concepts, a brief overview of the contributions which appeared in the literature in the last 15years is presented.

Large contributions to dark matter annihilation from three-body final states

The annihilation rate of dark matter particles plays a crucial role in dark matter studies, for it determines their relic density and their indirect detection signal. In this paper, we show that this annihilation rate can receive large additional contributions from three-body final states consisting of a real and a virtual massive particle, such as WW* (Wf \bar f') and t \bar t* (tW\bar b). We consider two specific examples, from the singlet model and the MSSM, and find that, due to the new three-body final state contributions, the prediction for the relic density may decrease by more than a factor two, whereas the present dark matter annihilation rate gets enhanced by up to two orders of magnitude. Some of the implications of these results are briefly discussed.

First principle calculations of core-level binding energy and Auger kinetic energy shifts in metallic solids

We present a brief overview of recent theoretical studies of the core-level binding energy shift (CLS) in solid metallic materials. The focus is on first principles calculations using the complete screening picture, which incorporates the initial (ground state) and final (core-ionized) state contributions of the electron photoemission process in X-ray photoelectron spectroscopy (XPS), all within density functional theory (DFT). Considering substitutionally disordered binary alloys, we demonstrate that on the one hand CLS depend on average conditions, such as volume and overall composition, while on the other hand they are sensitive to the specific local atomic environment. The possibility of employing layer resolved shifts as a tool for characterizing interface quality in fully embedded thin films is also discussed, with examples for CuNi systems. An extension of the complete screening picture to core–core–core Auger transitions is given, and new results for the influence of local environment effects on Auger kinetic energy shifts in fcc AgPd are presented.

O- and H-induced surface core level shifts on Ru(0001): prevalence of the additivity rule

In previous work on adsorbate-induced surface core level shifts (SCLSs), the effectscaused by O atom adsorption on Rh(111) and Ru(0001) were found to be additive:the measured shifts for first-layer Ru atoms depended linearly on the number ofdirectly coordinated O atoms. Density-functional theory calculations quantitativelyreproduced this effect, allowed separation of initial- and final-state contributions, andprovided an explanation in terms of a roughly constant charge transfer per Oatom. We have now conducted similar measurements and calculations for threewell-defined adsorbate and coadsorbate layers containing O and H atoms:(1 × 1)-H,(2 × 2)-(O+H)and (2 × 2)-(O+3H) on Ru(0001). As H is stabilized in fcc sites in the prior two structures and in hcp sites inthe latter, this enables us to not only study coverage and coadsorption effects on theadsorbate-induced SCLSs, but also the sensitivity to similar adsorption sites. Remarkablygood agreement is obtained between experiment and calculations for the energies andgeometries of the layers, as well as for all aspects of the SCLS values. The additivity of thenext-neighbor adsorbate-induced SCLSs is found to prevail even for the coadsorbatestructures. While this confirms the suggested use of SCLSs as fingerprints of the adsorbateconfiguration, their sensitivity is further demonstrated by the slightly differentshifts unambiguously determined for H adsorption in either fcc or hcp hollowsites.

Origin of XPS binding energy shifts in Ni clusters and atoms on rutile TiO 2 surfaces

Cluster-size-dependent binding energy (BE) shifts of Ni 2p 3/2 spectra in Ni clusters with respect to bulk Ni metal have been studied as a function of Ni coverage on clean rutile TiO 2(0 0 1) and TiO 2(1 1 0) surfaces at room temperature. As a common method to distinguish initial and final state contributions to the core-level binding energy shifts in clusters, Auger parameter (AP) analysis of photoelectron spectra has been employed and reveals an obvious initial state contribution at the coverage of 0.5 monolayers (ML). From a comparison of results for TiO 2(0 0 1) and (1 1 0) surfaces, the initial state effect is demonstrated to be strongly affected by the substrate and is assigned to a combination of eigenvalue shift in surface core-level shift (SCLS) and charge transfer between the metal clusters and substrates. The Ni 2p 3/2 BE’s of atomic Ni on TiO 2(0 0 1) and (1 1 0) surfaces are deduced to be 853.69 and 853.55 eV, respectively, from an extrapolation of the experimental BE curves to zero Ni coverage. Compared with atomic Ni in gas phase, relaxation shifts of 7.34 and 7.48 eV are obtained on TiO 2(0 0 1) and (1 1 0) surfaces, respectively. These values are very close to the relaxation shift of 7.3 eV due to d electron screening, indicating d-like screening effects from the TiO 2 substrates after Ni 2p photoionization.

Electronic structure and magnetic properties of the compound CeCuIn

Magnetization, magnetic susceptibility, electrical resistivity, thermoelectric power and X-ray photoemission measurements were performed on a polycrystalline sample of CeCuIn. This compound crystallizes in a hexagonal structure of the ZrNiAl type. The magnetic data indicate that CeCuIn remains paramagnetic down to 1.9 K with a paramagnetic Curie temperature of −13 K and an effective magnetic moment equal to 2.5 μ B. The electrical resistivity has metallic character, yet in the entire temperature range studied here, it is a strongly nonlinear function of temperature. The temperature dependence of the thermoelectric power is dominated by a small positive maximum near 76 K and a deep negative minimum at about 16 K. Above 150 K the thermopower exhibits a Mott's type behavior. The positive sign of the Seebeck coefficient in this temperature region indicates that the holes are dominant charge and heat carriers. The structure of Ce 3d 5/2 and Ce 3d 3/2 XPS spectra has been interpreted in terms of the Gunnarsson–Schönhammer theory. Three final-state contributions f 0, f 1 and f 2 are clearly observed, which exhibit a spin–orbit splitting Δ SO≈18.7 eV. The appearance of the 3d 9f 0 component is a clear evidence of the intermediate valence behavior of Ce. From the intensity ratio I(f 0)/[ I(f 0)+ I(f 1)+ I(f 2)] the 4f-occupation number is estimated to be 0.95. In turn, the ratio I(f 2)/[ I(f 1)+ I(f 2)]=0.08 yields a measure of the hybridization energy that is equal to 45 meV.

An experimental study of charge distribution in crystalline and amorphous Si nanoclusters in thin silica films

Crystalline and amorphous nanoparticles of silicon in thin silica layers were examined by transmission electron microscopy, electron energy loss spectroscopy, and x-ray photoelectron spectroscopy (XPS). We used XPS data in the form of the Auger parameter to separate initial and final state contributions to the Si2p energy shift. The electrostatic charging and electron screening issues as well as initial state effects were also addressed. We show that the chemical shift in the nanocrystals is determined by initial state rather than final state effects, and that the electron screening of silicon core holes in nanocrystals dispersed in SiO2 is inferior to that in pure bulk Si.

Disorder broadening of alloy Auger spectra

Auger spectroscopy promises the means to separate initial and final state contributions to the disorder broadening of core XPS spectra in disordered alloys. Auger disorder broadening, deduced from recent ab initio results, is predicted to be greater than XPS disorder broadening for Cu 50Pd 50 and Ag 50Pd 50 alloys. Simulations are used to assess whether this effect is observable experimentally despite the greater lifetime broadening of Auger spectra. A number of cases where narrow core–core–core Auger transitions should allow clear experimental identification of this effect are identified. The prospects for determining environment-resolved Auger spectra using APECS have been investigated.

Initial and final state contributions to binding-energy shifts due to lattice strain: Validation of Auger parameter analyses

The validity of Auger parameter analyses to separate initial and final state contributions to core-level binding energy shifts in the growth of nanoparticles is tested; the specific concern is shifts due to lattice strain. Theoretical energies for the hole-states involved are used to avoid the approximations and assumptions normally required to justify the analyses. When the Auger transitions involve states with high lying d-holes, the Auger parameter analysis of the origin of the shifts is incorrect. When only core–hole Auger states are used, a suitable formulation will accurately reproduce the initial state origin of shifts due to lattice strain.

Synchrotron radiation x-ray photoelectron spectroscopy of Si nanocrystals grown onto Al2O3∕Si surfaces

Synchrotron radiation x-ray photoelectron spectroscopy is used for the study of 5 nm Si nanocrystals (NCs) for applications in nonvolatile memory devices. A detailed peak shape analysis of the high-resolution Si2p core-level spectra reveals average chemical shifts for the oxidized components consistent with those observed for planar oxidation. However, a much larger Gaussian width is found for each spectral component, reflecting the important level of structural disorder in the NCs, arising from stress produced during the kinetics of the oxide shell growth. Final state contributions to the core-level spectra are also discussed.

Ab initiostudy of disorder broadening of core photoemission spectra in randomCu−PdandAg−Pdalloys

A first-principles study of the effect of local environment on the electronic structure of random face-centered cubic $\mathrm{Ag}\ensuremath{-}\mathrm{Pd}$ and $\mathrm{Cu}\ensuremath{-}\mathrm{Pd}$ alloys is presented. The core-level shift for each atom in the equiatomic alloys is calculated and compared to experimental data. It is shown how the initial-state and final-state distributions contribute to the total broadening. We find that the initial-state and the final-state contributions together increase the broadening for the investigated core levels in Cu and Ag, whereas they cancel each other to a large degree for Pd. We also demonstrated how local lattice relaxations influence the binding energy shift. We find that relaxation does not influence the average shift, though it is able to affect the broadening of the simulated x-ray photoelectron spectroscopy spectra.

Quantum momentum distribution and kinetic energy in solid 4He.

We present measurements of neutron scattering from solid 4He at high momentum transfer. The solid is held close to the melting line at molar volume 20.87 cm3/mol and temperature T=1.6 K. From the data, we determine the shape of the momentum distribution, n(k), of atoms in the solid and the leading final state contribution to the scattering. We show that n(k) in this highly anharmonic, quantum solid differs significantly from a Gaussian. The n(k) is more sharply peaked with larger occupation of low momentum states than in a Maxwell-Boltzmann distribution, as found in liquid 4He and predicted qualitatively by path integral Monte Carlo calculations. The atomic kinetic energy is <K>=(24.25+/-0.30) K. If n(k) is assumed to be Gaussian, as is usually the practice, a <K> 10% smaller is obtained.

XPS study of Cu/substrate systems obtained by pulsed laser deposition

AbstractIn this paper XPS was used to study the evolution of Cu 2p3/2 peaks with the increase of the metal coverage on different types of substrate: Ni, HOPG (highly orientated pyrolytic graphite) and KBr. The results showed that: (i) the binding energy of the Cu 2p3/2 peak in the system Cu/HOPG decreases with surface coverage, while in the system Cu/Ni it increases; (ii) with the increase of the Cu coverage in all the systems studied a general trend of the Cu 2p3/2 peak is the reduction of FWHM (full width at half maximum), but the degree of the FWHM change depends greatly on the type of the substrate. The results obtained for binding energy change are discussed in relation to the initial and final state contributions. The results indicate that the final state contributes more to the change of the binding energy in the more 3‐dimensional structure Cu/HOPG system, while in the more 2‐dimensional Cu/Ni system the initial state contribution dominates. The FWHM change is analysed in terms of the size distribution of clusters and change of the lifetime of the holes left by the photoelectrons, which is affected by the size of the clusters and the degree of the hybridization between the s and d electrons. Copyright © 2004 John Wiley &amp; Sons, Ltd.

Final state contribution to the Si 2p binding energy shift in SiO 2/Si(1 0 0)

The Si 1s and 2p photoemission and the Si KL 2,3L 2,3 Auger emission from SiO 2/Si(1 0 0) surfaces were measured for oxide thicknesses from 0.4 to 3.8 nm using high-energy photoemission ( hν=3000 eV). The energy of the SiO 2 emission depends on the layer thickness. The Si 4+–Si 0 energy differences Δ E 1s, Δ E 2p and Δ E KLL were combined to separate the initial and final state contribution to the energy shift of the Si 4+ 2p line. Within the experimental error, the 2p initial state is constant up to about 2 nm oxide thickness, where differential charging gradually sets in. The observed variation of Δ E 2p is entirely due to final state relaxation. It is found that Δ E 1s−Δ E 2p=0.62 eV, independent of the oxide thickness.