X-ray photoelectron spectroscopy using hard X-rays

Journal of Electron Spectroscopy and Related Phenomena 178–179 (2010) 241–257

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X-ray photoelectron spectroscopy using hard X-rays László Kövér Institute of Nuclear Research of the Hungarian Academy of Sciences, 18/c Bem tér, H-4026 Debrecen, Hungary

a r t i c l e

i n f o

Article history: Available online 22 December 2009 Keywords: X-ray photoelectron spectroscopy Hard X-ray excitation Surface/interface chemical analysis Buried interfaces Bulk electronic structure of solids

a b s t r a c t Hard X-ray photoelectron spectroscopy (HAXPES or HXPS), using hard (2–15 keV) X-rays for excitation and high energy resolution, has shown a spectacular development recently, due to its capability for providing an insight into the bulk electronic structure of solids and the chemical composition of buried layers and interfaces lying at depths of several tens of nm. Following a summary of fundamentals concerning photoionization phenomena and transport processes of photoelectrons induced by hard X-rays from solids, examples of core level and valence band HAXPES spectra are presented to illustrate different physical effects. Examples are given of applications of HAXPES in determining electronic structure properties and in surface/interface chemical analysis of material systems of high practical interest. Finally, some perspectives for further developments are outlined. © 2010 Elsevier B.V. All rights reserved.

1. Introduction In the last few years a quick development and an increasing interest are witnessed in the field of X-ray photoelectron spectroscopy induced by hard X-rays from solids (hard X-ray photoelectron spectroscopy, HAXPES or HXPS). It is interesting to note that the first observation of the (Cu metal to CuO) chemical shift of the Cu 1s shell electron binding energy was observed by using hard (Mo K␣1 ) X-rays for excitation of photo- and Auger electrons [1]. As a consequence of the need for high energy resolution and surface sensitivity, however, since then the conventional laboratory X-ray photoelectron spectrometers are using Al K␣ (non-monochromatized or monochromatized) or Mg K␣ radiation for excitation. The availability of synchrotron photon sources, providing tunable, monochromatic and polarized photon beams, opened new possibilities for HAXPES and in spite of the very low photoionization cross-sections (two orders of magnitude lower, on the average, compared to those at the energy of the conventional Al K␣ or Mg K␣ photon sources) at the exciting photon energy of 8 keV, the feasibility of this kind of spectroscopy was demonstrated for core levels (Au 4f, Ag 3d) very early [2]. The real exploitation of this technique started, however, only well after the appearance of the 3rd generation synchrotrons, due to the rather demanding requirements necessary to be satisfied concerning the experimental conditions for a high energy resolution, high photoelectron yield experiment. Such requirements are: high energy resolution, high flux and brilliance photon beamline, high stability and low noise electron spectrometer (including high performance, high energy

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resolution electron energy analyzer adapted to the size of the photon beam spot and fast electron detector system), operating in the electron kinetic energy region up to 10–15 keV, possibility for grazing incidence photon beam excitation. These requirements can be met only since the last few years due to the great progress in the development of synchrotron beamlines, electron spectrometers, detectors and precision electronics. It should be noted that laboratory equipments with non-monochromatized or monochromatized hard X-ray sources are also used for specific photoelectron or Auger electron spectroscopic measurements [3–5], such as determining charge transfer from metal–alloy Auger parameter shifts, studying solid-state effects on deep core Auger transitions of 3d metals or performing photoelectron spectro-holography. What are the main benefits of the hard X-ray photoelectron spectroscopy of solids? First of all the significantly increased information depth (in the range of several times 10 nm) allowing to collect information (in a non-destructive way) on bulk electronic structure or on chemical composition of deeply buried interfaces. The dominance of bulk components and the suppression of surface components in the valence band photoelectron spectra greatly facilitate the interpretation and the experimental spectra are well approximated by the calculated bulk density of states weighted with the partial atomic photoionization cross-sections. At the same time, using grazing incidence X-ray beams for excitation, an extreme surface sensitivity can be achieved. Due to the significant decrease in the cross-sections for electron scattering with increasing electron energy, the distortion of the photoexcited electron spectra (lineshape) attributable to electron scattering within the solid samples, is also decreasing. As a consequence, quantitative surface/interface analytical applications and interpretation of ARXPS spectra are expected to be easier. Deep core shells are accessible, it is easier to avoid the overlap between photoelectron and

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Auger spectra, the validity of the simple atomic structure models for interpreting Auger parameter shifts can be assumed. For ordered systems, the angular distribution of hard X-rays induced and diffracted high energy photoelectrons is more sharp in the forward direction and the structure due to higher order diffraction is considerably weaker than in the case of using lower (1–2 keV) energy X-rays for excitation. Hard X-rays produce standing waves with much stronger modulations as a function of the depth measured from the surface, providing better conditions for obtaining accurate information on the position of component atoms and the site specific local electronic structure from photoelectron spectra. These advantages ensure unique conditions for a number of applications with great practical significance, such as monitoring bulk electronic structure of advanced materials (including, e.g., high critical temperature superconductors, new materials for optoelectronics and information technology, new photovoltaic materials), non-destructive depth profiling of film solar cell structures and semiconductor multilayer (high-k/metal gate) stack microelectronic devices of ca. 20 nm thickness. This paper does not intend to provide a complete picture of the progress in the field—for the readers looking for such reviews excellent recent reports [6–8] are recommended. On the contrary, in the following first fundamental processes, accompanying photoionization induced by hard X-rays from solids are discussed continuing with different excitation and transport processes of high energy electrons within the solid, focusing on the energy dependence of these processes. Then the characteristic electronic structure information reflected by photoelectron and Auger spectra excited from different systems using hard X-rays, is demonstrated, finally selected examples are given for applications of HAXPES. Photoelectron diffraction/holography and X-ray standing wave excited photoemission using hard X-rays are discussed elsewhere [8] including papers in this Special Topical Volume [9,10]. Here mainly the aspects of HAXPES important for quantitative applications of surface chemical analysis are emphasized.

2. Fundamentals of hard X-ray photoelectron spectroscopy of solids 2.1. Photoionization using hard X-rays Considering the available theoretical models describing photoemission, including the differential cross-section of photoionization for photon energies in the 2–15 keV range, the model based on the power series expansion of the electron–photon interaction operator [11] is applied frequently, in spite of using often only a limited number of terms of the expansion (the electric dipole and quadrupole operators are related to the first and second terms, while the third and fourth terms are associated with the magnetic and electric dipole operators, respectively). A more sophisticated expansion of the electron–photon interaction operator is the irreducible tensor expansion method developed by Fujikawa et al. [12–14]; this model accounts for all electric dipole operators as well as other multipole terms. These models predict that in the case of using high energy X-rays for excitation of photoelectrons, beyond the electric dipole transitions, contributions from electric quadrupole and magnetic dipole transitions become nonnegligible, even significant. Detailed calculations [14] show that – as a consequence of opposite effects of various types of errors of different sources in this approximation – the model based on the multiple power series expansion of the electron–photon interaction operator [11] still works well up to ca. 10 keV photon energy in many cases.

2.1.1. Photoionization cross-sections: dependence on photon energy The tabulation of Scofield [15] contains calculated photoionization cross-section data for free atoms with atomic number 1–101 and for photon energies 1–1500 keV. In these calculations – accounting for all multipole orders of the photon field – the electrons in the initial and final states are treated relativistically and assumed to move in the same central Hartree–Dirac–Slater potential of the neutral atom. Using the same atomic model, the effect of the hole produced following photoionization of the particular atomic shell is taken into account in the frozen orbital approximation in the calculations and tabulated data of Trzhaskovskaya et al. [11] for nine photoelectron kinetic energies in the range of 0.1–5 keV (in the atomic number range 1–54 for all subshells [11a], while in the case of higher atomic numbers in the range of 55–100 [11b], for subshells with electron binding energies lower than 2 keV). These data have recently been completed by further data for four values of photoelectron kinetic energies in the range 1–10 keV in the case of atomic subshells with binding energy lower than 2 keV for all atoms with atomic numbers in the range of 1–100 [11c]. The comparison of Scofield’s and Trzhaskovskaya’s subshell photoionization cross-section data shows that taking the hole into account can lead to differences less than 12% [16]. In molecules or solid compounds the effective charges on the component atoms and – reflecting the charge reorganization – the spatial distribution of the atomic orbitals can differ significantly from those on neutral atoms, and the contraction or expansion of the atomic orbitals can result in small changes in the corresponding photoionization cross-sections [16]. The subshell photoionization cross-sections are strongly decreasing with photon energy; this is the reason why high photon flux is needed for HAXPES. The extent of the decrease is, however, different for atomic subshells having different principal and angular momentum quantum numbers, leading (as a consequence) to considerable variation of certain cross-section ratios as a function of photon energy in the hard X-ray regime. In Fig. 1 the photon energy dependence of selected subshell cross-section ratios is shown in the case of particular atoms. It can be seen from the figure that at higher photon energies the drop in the cross-sections is smaller for high principal and low angular momentum quantum number subshells and the change in the respective cross-section ratios can reach one order of magnitude in the photon energy range of 10–15 keV. This character of energy dependence of cross-section ratios provides a possibility (changing the photon energy) to selectively enhance or suppress the excitation of photoelectrons from atomic orbitals

Fig. 1. Photon energy dependence of ratios of subshell photoionization crosssections for selected atoms. The cross-section data were taken from Ref. [15].

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with given symmetries, that could give very useful information in exploring atomic, molecular and electronic structure of complex solid materials. In the case of valence band XPS spectra of (e.g., polycrystalline) solids, the intensity distribution of the photoelectrons (apart from the contribution of the electrons scattered inelastically in the solid sample) can be approximated as the sum of the different angular momentum projected partial density of electronic states (PDOS) weighted by their respective transition probabilities into a plane wave final state [18,19]: I(E, h) ∝



i,l (E)i,l (E, h)

(1)

i,l

where i, l is the individual, l angular momentum projected singleparticle partial density of states of the ith atom and  i,l is the respective angle integrated angular momentum dependent subshell photoionization cross-sections. In the molecular orbital (MO) model the PDOS can be calculated using the Mulliken population analysis [17] and the intensity distribution of the valence band photoelectrons can be approximated by the Gelius formula [20,21]: Ik ∝



jA Pk,j,A

(2)

A,j

where Ik is the relative photoelectron intensity contribution from the kth MO, jA are the subshell photoionization cross-sections for the jth atomic orbital (AO) of atom A and Pk, j, A are the respective Mulliken population contributions of the jth AO of atom A to the kth MO. The contributions from different orbitals are energy broadened using Lorentzian or Gaussian distributions accounting for vibrational effects and effects of the finite energy resolution of the spectrometer. In high energy photoemission the effective decoherence due to the Debye–Waller factor improves the applicability of the Gelius formula [12], making the bulk sensitive valence band HAXPES attractive for obtaining electronic structure information in the case of complex materials. 2.1.2. Angular distribution of photoelectrons: the role of non-dipole effects The angular distribution of the photoelectrons in the case of free atoms and circularly polarized or unpolarized photons can be described by the formula developed by Cooper [21]: di  = i 4 d˝



ˇ 1 − P2 (cos ) + 2

Fig. 2. Calculated angular distributions for different energy Cu 1s photoelectrons. The differential photoionization cross-section data were taken from Ref. [11].

 2

2





sin  + ı cos 

photon energies higher than a few keV and quickly increase further with increasing photon energy above 10 keV [11]. In addition to the first order terms with the non-dipole parameters appearing in Eqs. (3) and (4), second order terms (including octupole effects with additional non-dipole parameters) may also contribute significantly to the angular distributions [11c,22]. These contributions may be of the order of several percent for unpolarized radiation and may reach about 10% in the case of linearly polarized radiation at 10 keV photoelectron energy [22]. Fig. 2 shows the calculated angular distributions for different kinetic energy Cu 1s photoelectrons (differential photoionization cross-section data were taken from Ref. [11]). It can be clearly seen from Fig. 2 that the angular position of the maxima of the distribution is increasingly shifted with the electron energy. The energy dependence of this shift in the angular position of maxima is demonstrated in Fig. 3 for photoelectrons excited from different subshells of C, Si, Fe, Cu, Ge and Au atoms. The angular shift data (derived from data in Ref. [11]) presented in Fig. 3 show quite large shifts at high electron energies, especially for higher angular momentum subshells and higher atomic numbers. This indicates that the neglect of non-dipole effects on the angular distributions

(3)

where d i /d˝ is the differential photoionization cross-section for the ith atomic subshell,  i the total photoionization cross-section for the same subshell, P2 the 2nd Legendre polynomial,  the angle between the electron and photon propagation (the direction of the respective vectra of their momenta), ˇ is the parameter for describing dipolar,  and ı are parameters for describing non-dipolar effects. For linearly polarized photons the angular distribution is given as [21]:  di = i [1 + ˇP2 (cos   ) + (ı + cos2   )sin  cos ϕ] 4 d˝

(4)

where   is the angle between the photon polarization vector and the electron momentum vector and ϕ is the angle between the photon momentum vector and the plane containing the electron momentum vector and the photon polarization vector. All parameters depend on photon energy. The tabulations of Trzhaskovskaya et al. [11] contain data for the dipole and non-dipole parameters for all atomic subshells included, in the case of photoelectron kinetic energies 0.1–10 keV. Although non-dipole effects are present and for some subshells are observable at lower photon energies, their contributions to the angular distributions become significant for

Fig. 3. Angular positions of the maxima of the angular distributions of the C 1s, Si 1s, Cu 2p, Ge 2s and Au 4f photoelectrons as a function of electron kinetic energy. The respective differential photoionization cross-section data were taken from Ref. [11].

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in the case of interpreting angular resolved HAXPES results may lead to erroneous conclusions. 2.1.3. Effects of atomic recoil on photoemission from solids In the case of high energy photoelectrons emitted from (especially low atomic number) atoms, the effects of atomic recoil can be observed. Using the single site approximation for describing phonon excitations by the recoiled X-ray absorbing atom embedded in a solid, as well as the Debye approximation for calculating the recoil energy shift Er and the energy broadening Er the recent model of Fujikawa et al. [13,23] provides: Er = −

Q2 2M

(5)

where Q = q − k (q is the photon momentum and k is the momen tum of the photoelectron) and Q ≈ 2(¯hω − Eb ), Eb denoting the binding energy of the electron for the particular subshell, ω the photon energy and M is the mass of the emitter atom. The energy broadening can be obtained as [23]:

2

( Er )  =

Q 2 (kB T ) 2MωD

2



/T

dxx

3 ıu2 MωD ex + 1 + x e −1 4

0



/T

dx sin4

is coupled with the crystal lattice and its wave function follows adiabatically the atomic motion [26].

 Tx  2

0

ex + 1 × x(ex − 1)

(6)

where T is the temperature,  the Debye temperature, ıu the nuclear displacement following the production of the core hole, kB the Boltzmann constant and ωD = kB . The full width at half maximum of the energy distribution broadening  the photoelectron 2

peak due to atomic recoil is FWHM = 2.35 ( Er ) . At higher temperatures, the energy broadening due to atomic recoil can be approximated by a simple formula [23]: 2

( Er )  =

Q 2 kB T M

(7)

Table 1 gives example values for the energy shifts and broadenings (FWHM) calculated or estimated using the model above. The energy shift data in Table 1 are comparable to chemical shifts in the case of lower atomic number elements indicating that neglecting effects of atomic recoil may cause problems in identification of the chemical state of component atoms in solids. Beyond the single site approximation, elastic scattering of photoelectrons on neighbor atoms can also be described by a model developed recently [24,14]. Recoil effects in C 1s HAXPES spectra of graphite were observed and quantitatively interpreted by Takata et al. [25] obtaining a recoil energy shift of 0.36 eV at 8 keV photon energy, in good agreement with the data in Table 1. In their recent high energy resolution HAXPES work [26] they reported observation of shifts of the Fermi edge in the photoelectron spectra of a polycrystalline Al film due to recoil effects in Al metal, indicating that the electron Table 1 Energy shift ( E, eV) and energy broadening (FWHM, eV) of photoelectron lines (excited from solids) due to atomic recoil. h = 5 keVa E Li 1s Be 1s C 1s (graphite) Si 1s Ge 2s a b c

h = 10 keVb FWHM

c

0.44 0.34 0.25 0.07 0.03c

c

0.40 0.40 0.28 0.17 0.11c

Taken or calculated from data given in Ref. [23]. Taken or calculated from data given in Ref. [13]. Estimated values Using Eq. (7).

Fig. 4. Summary of main types of excitation processes accompanying photoionization and photoemission in solids.

E

FWHM

0.95 0.72 0.53 0.23c 0.09c

0.52 0.56 0.56 0.36c 0.22c

2.1.4. Excitations accompanying photoionization in solids The main types of excitations accompanying photoionization in solids are summarized in Fig. 4. These excitation processes can lead to appearance of satellite lines or additional structures in the energy loss part of the photoelectron or Auger electron peaks in the X-ray excited electron spectra. Some of these excitations are connected with the creation of the core hole in the atom emitting the photoor Auger electron, e.g., in the case of the shake processes, during the photoemission, an outer shell electron is excited from an occupied to unoccupied bound (shake up) or free (shake off) electronic state. In photoelectron spectra, the shake up process leads to satellites on the higher binding energy side of the peaks and the shake off electrons contribute to the continuous inelastic background, while in the photon excited Auger spectra both shake processes lead to satellite peaks. In addition, in the case of core Auger spectra, such as the KLL Auger spectra of Ni metal, not only the occurrence of the initial state core hole, but the final state core holes as well can induce, e.g., shake up satellites [27]. Utilizing the tunable and high energy resolution hard X-ray photon beams available at 3rd generation synchrotrons, the identification and separation of these different excitation processes are facilitated by the different nature of the intensity evolution of these satellites with photon energy near the X-ray absorption threshold of the inner shell containing the initial state core hole [27]. It should be noted, that in the case of 3d metals the satellite-main line energy separations are considerably larger for the KLL Auger transitions, than for the corresponding K-X-rays. The study of shake up satellites of deep core shell XPS peaks can be helpful for understanding the differences in screening and localization of different (including 1s) inner shell core holes, such investigations require monochromatized hard X-rays and high energy resolution electron spectroscopy. In order to obtain information on the bulk electronic structure, the kinetic energy of the emitted photoelectrons should be high enough. A recent example is the case of the Ni 1s and Ni 2p photoelectron spectra excited by 12.6 keV energy photons from a 50 nm thick metallic layer on Si (1 1 1) substrate: comparing the shapes of the Ni 1s and 2p main and satellite peak HAXPES spectra to model spectra obtained using the Charge-Transfer Multiplet theory, the physical mechanism leading to different satellite-main peak energy separations, has been identified [28]. In addition to the shake excitations discussed above, the appearance of the core hole can lead to collective excitation of the free or weakly bound electrons (longitudinal electron density oscillations that are quantized and the quanta are the plasmons)

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and these excitations are manifested in the photoelectron or Auger spectra as contributions to the energy loss structure [29]. The core hole induced intrinsic type excitations (Fig. 4.) include the shake and intrinsic plasmon excitations, while the extrinsic type (such as plasmon) excitations are connected with the interactions of the emitted photo- or Auger electrons during their transport in the solid towards the surface and with their escape from the solid [29]. While the excitations of bulk plasmons occur inside the solid, near the surface a different plasmon excitation mode occurs that is limited to two-dimensional charge density oscillations. As a result, characteristic surface plasmon satellite peaks in the energy loss part of the photoelectron or Auger lines, appear [30,31]. Due to core hole creation, electron transport and emission, multiple plasmon excitations can take place and interference phenomena between surface and bulk as well as intrinsic and extrinsic plasmon excitations can influence the shape of the observable electron spectra. In general, the interference terms are dependent on electron energy and significantly decrease at high energies; however, in the high energy region the decrease is weaker and the interference terms remain non-negligible [32,33,14]. 2.2. Transport of high energy photoelectrons in solids The transport processes for photo- or Auger electrons in solids can be characterized by several physical parameters, the most important parameters are defined and summarized in Table 2 (detailed information on these quantities can be found in the review of Powell and Jablonski [34]). For describing the probability of electron elastic scattering the differential cross-section for elastic electron scattering (DCS) is used, while the mean free path between two large angle elastic collisions is given by the transport mean free path (TrMFP) which can be calculated from the transport cross-section. It should be noted that the transport crosssection and transport mean free path appear in many analytical expressions describing electron transport in solids and are used in various quantitative analytical applications of XPS and Augerelectron spectroscopy [34]. The inelastic mean free path (IMFP) and the volume energy loss probability for an individual inelastic scattering event per unit path length and energy (DIIMFP) characterize the inelastic electron scattering processes in the bulk of a solid, while the corresponding parameters (surface excitation parameter, SEP, and the probability of surface excitations, i.e., the distribution of the probability of single energy loss events (per unit energy) resulting from surface effects at the surface crossing of an emitted electron, DSEP) describe excitations taking place near the surface upon photoelectron or Auger emission from the solid. A useful further parameter indicating the role of elastic scattering during electron transport is the single scattering albedo, defined

Table 2 Physical parameters and distributions characterizing electron transport in solids. DCS: differential cross-section for elastic electron scattering TrMFP: transport mean free path (tr = 1/(M tr ); tr = 4(1 − cos )(d/d˝)d˝;  tr : transport cross-section; M: atomic density; d/d˝: differential cross-section for elastic electron scattering) IMFP: inelastic mean free path (mean free path of electrons for inelastic scattering) SEP: surface excitation parameter (average number of surface excitations at a single surface crossing of an electron) DIIMFP: differential inverse inelastic mean free path DSEP: differential surface excitation parameter The IMFP, DIIMFP, SEP and DSEP can be derived from electron backscattering experiments. EAL: effective attenuation length (a parameter which, when replacing the IMFP in an expression derived from the common AES or XPS formalism (where elastic electron scattering is neglected) for a given quantitative application, will correct this expression for elastic-scattering effects [34])

245

as ω=

tr tr + 

(8)

where tr is the transport mean free path and  is the IMFP. Instead of the IMFP, however, in the practical quantitative chemical analysis of surface and interface layers using XPS or AES, another parameter, the effective attenuation length (EAL), that accounts for the effect of elastic electron scattering is used, and with this replacement, the expressions neglecting elastic-scattering effects are expected to be corrected for this effect. It should be noted, that the EAL may depend on the given quantitative analytical application, e.g., in the case of determining overlayer thickness using XPS, the EAL may depend on the layer thickness, the take-off angle and the angular distribution of the photoelectrons. 2.2.1. Energy dependence of electron transport parameters for elastic electron scattering Fig. 5a–c shows the DCS for Si, Cu and Au atoms as a function of the polar angle of scattering for selected electron energies (the relativistic DCS data were taken from the NIST Electron Elastic-Scattering Cross-section Database [35], DCSs were calculated using a scattering potential obtained from the self-consistent Dirac–Hartree–Fock electron density for free atoms [36] with the local exchange potential of Furness and Mc Carthy [37], and with the algorithm developed by Salvat and Mayol [38]). It can clearly be seen from the figures that although the DCSs are varying considerably at lower electron energies, for energies above 4 keV (Si, Cu) or in the case of the higher atomic number Au above 10 keV, the curves become smooth in the whole angular range. The energy dependence of the transport cross-sections (Fig. 6a) and the corresponding transport mean free paths (Fig. 6b) is presented in Fig. 6 [39] for the atoms C, Si, Ni, Pd and Pt, up to an electron energy of 10 keV, using the same NIST Database [35]. The data in Fig. 6 demonstrate that for both the transport cross-sections and the transport mean free paths, their energy dependence on the log–log plot can be described by approximately linearly decreasing (transport cross-sections, Fig. 6a) or increasing (transport mean free paths, Fig. 6b) functions with increasing electron energy, in the electron energy range above 2 keV. In this energy range, the values of the transport cross-section are larger, while the values of the transport mean free path are smaller for atoms with higher atomic numbers. For calculating transport cross-sections using the Dirac–Hartree–Fock potential for elements H–U, analytical expressions have recently been reported for electrons with energies 50 eV to 30 keV [40]. 2.2.2. Energy dependence of electron transport parameters for inelastic electron scattering in solids The shape of the DIIMFP distributions is almost independent on the electron energy, especially in the energy region higher than 2 keV [41]. Similarly, the shape of the DSEP distributions was found to be insensitive to the electron energy [42]. In Fig. 7 the normalized DIIMFP and DSEP derived from the analysis of pairs of REELS spectra of polycrystalline Au, using primary electron energies of 1–3.4 keV and 5–40 keV, respectively, are compared [43]. Within the accuracy of the experiment, the corresponding energy loss distributions are in a good agreement, the larger noise in the data in the case of the DSEP derived from the REELS spectra excited using high primary electron energies is attributable to the very small contribution from surface excitations to the spectra [43]. Integrating the DIIMFP over energy losses, the inverse IMFP is obtained. The calculated and experimental data for polycrystalline Al, Si, Cu and Au [44] presented in Fig. 8 show the linear increase of the IMFPs with increasing electron energy on the log–log plot in the energy range 2–20 keV, in a good agreement between theory

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Fig. 6. Dependence of the transport cross-sections (a) and the transport mean free paths (b) on the electron energy, for the atoms C, Si, Ni, Pd and Pt [39].

plasmons excited by the electron at surface crossing and its value can be greater than unity for electrons travelling almost parallel to the surface, indicating that surface excitations are most probable in this particular case [50]. The tendency in the values for the SEP as a function of energy (linear dependence on electron energy using a log–log plot presentation) is very similar for the materials selected [50,51] and decreases strongly with increasing electron energy, as can be seen in Fig. 9. For electrons the probability of crossing the surface boundary without exciting surface plasmons is proportional to exp(−SEP), where SEP depends on the energy of the electron and the angle of surface crossing, as a result, the intensity

Fig. 5. Differential cross-sections for elastic electron scattering for (a) Si, (b) Cu and (c) Au atoms, as a function of the polar angle of scattering for selected electron energies (the DCS data were taken from the NIST Electron Elastic-Scattering Crosssection Database [35]).

[44–49] and experiment in the range of higher electron energies, although it should be noted that there are only a few experimental data (see references in Ref. [44]) available in this region. The total probability of surface excitations induced by an electron crossing the surface of the solid once, i.e., the SEP, calculated using a quantum mechanical formalism for the self-energy of an electron interacting with the semi-infinite solid medium, on the basis of the dielectric theory, is compared in the case of solid Au, Ag, Cu, Ni, Fe and Ti for electrons escaping (single surface crossing) in the nearly normal and parallel directions, as a function of electron energy, as it is shown in Fig. 9 [50]. It should be noted that the SEP in the figure estimates the average number of surface

Fig. 7. Comparison of the normalized DIIMFP and DSEP derived from the analysis of pairs of REELS spectra of polycrystalline Au, using primary electron energies of 1–3.4 keV and 5–40 keV, respectively [43].

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Fig. 8. Energy dependence of electron IMFPs in polycrystalline Al, Si, Cu and Au [44]; solid curves: calculated values obtained using the optical-potential model of Bote et al., described in Ref. [44]; dashed curves: calculated values obtained using the relativistic optical-potential of Fernández-Varea et al. [45]; dot-dashed curves: calculated values obtained by Tanuma et al. [46–49] using the optical-data model; symbols: experimental data from the literature (for details on the sources of the data see Ref. [44]).

of the electrons is reduced by this factor (called surface correction factor) [52]. In quantitative applications of electron spectroscopy, however, usually the relative peak intensities are important, it is demonstrated in Ref. [52] that the relative surface correction factors (related to Ni reference) are approaching the unity with increasing electron energy and differ from unity by less than 10% at energies higher than 2 keV.

Fig. 9. Comparison of the surface excitation parameters (˘ s ) of solid Au, Ag, Cu, Ni, Fe and Ti for electrons escaping (single surface crossing) in the nearly normal and parallel directions, as a function of electron energy, calculated using a quantum mechanical formalism for the self-energy of an electron interacting with the semiinfinite solid medium, on the basis of the dielectric theory [50] (solid lines represent curve fitting).

The single scattering albedo, defined by Eq. (8) and often used in describing electron transport in solids, depends on the ratio of the transport (Fig. 6) and the inelastic (Fig. 8) mean free paths. Fig. 10 shows this ratio as a function of electron energy for selected elemental solids. The calculated TRMFPs are based on the NIST Electron Elastic-Scattering Cross-section Database [35] and the corresponding IMFPs were calculated using the TPP-2M formula [53]. It should be noted, that although the TPP-2M formula is expected to be valid only for electron energies below 2 keV, very recent estimations show that its average uncertainty is only about 11% for electron

Fig. 10. Ratio of the transport mean free path to the inelastic mean free path as a function of electron energy for selected elemental solids. The calculated TRMFPs are based on the NIST Electron Elastic-Scattering Cross-section Database [35] and the corresponding IMFP values are from calculations using the TPP-2M formula [53].

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(denoted by L) is given by [57,58]: L(t, ˛) = =

t 1

 cos ˛ ln Is0 − ln Ist 1 t

 cos ˛ ln ∞ ˚(z, ˛)dz − ln ∞ ˚(z, ˛)dz 0

Fig. 11. The single scattering albedo, ω, as a function of electron energy, for selected elemental solids (Si, Fe, Ni, Cu, Ge, Ag, W and Au, calculated using the electron elasticcross-section data given in Ref. [35] and the IMFP data derived from the TPP-2M formula [53]).

energies up to 30 keV in the case of most of the elemental solids [54,55]. From the data in Fig. 10, the energy dependence of the ratio seems close to a linear function, especially at energies higher, than 2 keV. Fitting the curves in Fig. 10 to linear functions, to a good approximation, the gradient parameters derived depend linearly on the inverse of the volume density of the solids, providing an easy quick estimate for the single scattering albedo, leading to an empirical expression: ω∼

1 (2.81 + (8.68/)E − 0.16E)

(10)

t

where t is the thickness of the overlayer, ˛ the angle of electron emission with respect to the surface normal, Is0 the measured XPS or Auger electron peak intensity of the pure substrate sample without the overlayer, Ist the measured peak intensity in the case of the substrate covered by an overlayer of thickness t, z the depth measured along the surface normal from the surface inward the solid and ˚(z, ˛) the probability that the electron, emitted from the surface in a specified state and direction and originated from a specified depth, i.e., the depth distribution function (DDF) [59]. Usually, for ˛ < 60◦ , L is only a relatively weak function of the emission angle and depends only slightly on the overlayer thickness in a large thickness range [56,60]. According to Eq. (10), for known overlayer thicknesses L can be determined from experiments measuring Is0 and Ist , or can be estimated from calculations of the DDF using analytical expressions [61] or the Monte Carlo simulation method [60]. For estimating R = L/, the ratio of the practical EAL to the IMFP, empirical expressions were proposed by Seah and Gilmore [62] (RSG ) and by Powell and Jablonski (RPJ ) [57,58,63]. The expression proposed by Seah and Gilmore is based on EAL values derived from Monte Carlo simulations of electron scattering in solids [64] for the case of photoelectrons excited from 27 elemental solids and in emission angle of 45◦ [62] (for electron energies below 2 keV): RSG = 0.979[1 − ω(0.955 − 0.0777ln Z)]

(9)

where  denotes the density of the material, given in g/cm3 units and E is the energy of the electron (keV). The dependence of the single scattering albedo (calculated using the electron elastic-cross-section data given in Ref. [35] and IMFP data from the TPP-2M formula [53]) on electron energy for selected elemental solids (Si, Fe, Ni, Cu, Ge, Ag, W and Au) is demonstrated in Fig. 11. As it can be seen from the figure, in the electron energy range above 2 keV, ω, with higher values for higher atomic number materials, decreases nearly linearly with increasing electron energy on a logarithmic scale, indicating the decreasing strength of the effects of elastic electron scattering at higher energies [34]. In the absence of elastic electron scattering in solids, the exponential attenuation of the intensity of photo- or Auger electrons induced at different depths in the material and travelling in the bulk region towards the surface, could be characterized by the IMFP and fairly simple intensity formulae could be used in many quantitative analytical applications. To account for the presence of elastic electron scattering complicates the situation, however, introducing a new electron transport parameter, the effective attenuation length (EAL), that is by definition a parameter correcting the expressions for XPS and AES intensities (derived neglecting elastic electron scattering) for effects of elastic scattering [34], the simple formalism used previously can be preserved. Unfortunately, the EAL is not a simple material parameter. It depends on the particular application and its different definitions can lead to different expressions [56–58]. For instance when describing the attenuation of photoelectrons emitted from a system consisting of a substrate covered by an overlayer, to obtain the thickness of the overlayer (the most common use of EAL), the EAL will depend on the thickness of the overlayer, the angle of electron emission and the angular distribution of the emitted photoelectrons. In this case the (“practical”) EAL

(11)

where Z is the atomic number. The standard deviation of the differences between the EALs derived from Eq. (11) and the EAL values derived from Monte Carlo simulations was 1.2% and the expression (11) was recommended for electron emission angles between 0◦ and 58◦ . On the basis of their calculations using the kinetic Boltzmann equation within the transport approximation, Powell and Jablonski proposed the following empirical formula for the case ˛ < 60◦ [57,58]: RPJ = 1 − Aω

(12)

The parameter A (the recommended value for A is 0.7 [57,58]) depends weakly on the electron emission angle and in the case of XPS on the angle between the directions of the exciting photon beam and the emitted photoelectrons. For a particular range of overlayer film thicknesses the average EAL, Lave (˛) can be determined from [63]: 1 1  n cos ˛ n

L˛ve (˛) =

i=1

ln

∞ 0

ti ˚(z, ˛)dz − ln

∞ ti



(13)

˚(z, ˛)dx

where ti is the ith thickness in a series of n uniformly distributed film thicknesses. It was found that Lave (˛) does not vary appreciably with ˛ in the electron emission angle range between 0◦ and ave (see Eq. 50◦ and for Lave / in the corresponding expression for RPJ (12)) the recommended value for the parameter A is 0.735 [63]. The calculated RSG and RPJ ratios obtained using Eqs. (11) and (12) [65] are compared (in the case of Ni, Cu and Ge and for electron energies (up to 15 keV)) in Fig. 12a (Ni), b (Cu) and c (Ge), as well as with data from experiments (LE /i ) [66,67], Monte Carlo simulations [68] and from the NIST EAL database [69]. As can be seen in the figures, the curves approach unity at high electron energies and the differences between the values obtained using the two formulae are smaller, than 2–3% [65]. The agreement between the calculated R ratios and

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249

Fig. 12. Comparison of calculated RSG and RPJ ratios obtained using Eqs. (11) and (12) [65] (in the case of Ni, Cu and Ge and in the range of electron energy up to 15 keV) for Ni (a), Cu (b) and Ge (c), as well as with data from experiments (LE /i )[66,67], Monte Carlo simulations [67] and from the NIST EAL database [68].

the available experimental results [66,67] is very good in the case of Cu and Ni and it is reasonable for Ge. The data derived from Monte Carlo simulation [68] confirm the tendency of the energy dependence predicted by the formulae and agree better with the experimental data. Below 2 keV electron energy, a good agreement of the calculated data is observed with data from the NIST EAL database [69]. These results demonstrate that with increasing electron energy (especially above 2 keV) the effects of elastic electron scattering are strongly decreasing and the simple expressions (11) and (12) provide a good approximation for the EAL for high electron energies range [65].

2.2.3. Effects of electron scattering on angular distributions of photoelectrons emitted from solids In a solid the angular distribution of photoelectrons emitted from embedded atoms is distorted as a consequence of the electron scattering processes taking place during the transport of the photo- or Auger electron towards the surface. Accounting for effects of electron elastic and inelastic scattering in the solid, the respective modified (original Eqs. (3) and (4)) differential subshell photoionization cross-section in the case of unpolarized photon excitation is given by Ref. [70]: disu

ai = 4 d˝



ˇ D1 − P2 (cos ) + 2

 2

2



sin  + ı cos 

 (14)

where a = 1 − ω, D1 = H(ω,˛)a0.5 and H is the Chandrasekhar function. An approximation of the Chandrasekhar function is [71]: H=

1 + 1.908˛ 1 + 1.908˛(1 − ω)0.5

(15)

A similar equation applies for the case of excitations using linearly polarized photons [70]: sp

di

d˝

=

ai [D1 + ˇP2 (cos   ) + (ı +  cos2   )sin  cos ϕ]. 4

(16)

2.2.4. Extrinsic and intrinsic plasmon excitations (surface and bulk): relative spectral contributions and interference effects In principle, the intrinsic and extrinsic excitations taking place upon the creation of the core hole (in the bulk or in the surface region of the solid) or during electron transport in the bulk or the surface layers of the material, are not separable [72–75]. However, the contribution of surface excitations to photoinduced electron spectra quickly decreases with increasing electron energy, as pointed out above. According to recent results of Novák [76], the neglect of interferences due to the interaction of the travelling electron with the electric field induced at the earlier stage of its trajectory does not cause significant errors in modeling electron transport in the case of solid Si, even at low (500 eV) electron energy. Fig. 13 shows the plasmon energy loss part of the calculated Al 2p photoelectron spectra for solid Al sample and 10 keV energy exciting X-rays linearly polarized in the x direction [77] and with neglect of the asymmetry of the core XPS peak and elastic electron

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Fig. 13. Bulk (at 15.8 eV) and surface (at 11.2 eV) plasmon loss regions of calculated Al 2p photoelectron spectra excited from metallic Al by 10 keV energy X-rays linearly polarized in the x direction, for photoelectrons emitted with a take-off angle of 60◦ in the xz plane (the z axis is parallel to the surface normal) [77].

scattering. The results [77] indicate a significant decrease of the relative importance of surface plasmon losses to that of bulk losses with increasing photoelectron energy, as expected. While destructive interference between extrinsic and intrinsic excitations plays an important role influencing strongly the shape of the spectra at low electron energy [78], the interference is much weaker in the case of bulk losses than for the surface losses and it is weakening further with increasing electron energy, although this tendency is rather slow at higher electron energies [77]. Using their dielectric response XPS model [75] and observing a good agreement [79] with experimental Mg K␣ X-rays excited Al 2s photoelectron spectra [80] measured at different electron emission angles, Yubero and Tougaard studied the contributions from extrinsic and intrinsic excitations to the spectra, finding that the intrinsic contribution to surface excitations is negligibly small, the shape of the intrinsic bulk plasmon peak is considerably more asymmetric than that of the extrinsic bulk plasmon peak and the relative intensity of the intrinsic bulk plasmon peak decreases towards grazing emission angles [79]. This dielectric response model predicted properly the increase of the intensity of the bulk plasmon peak in the Si 1s photoelectron spectra excited from a Si (1 1 1) single crystal when changing the photon energy from 3000 eV to 5500 eV [81] and the contribution of the bulk plasmon excitations to the Ge KL2 L3 Auger spectra photoexcited from polycrystalline Ge films [82]. 3. Hard X-ray photoelectron spectra There are different models available for interpreting quantitatively photoelectron and Auger electron spectra excited using hard X-rays. Simulations of lineshapes are usually based on the simplifying assumptions that the effects of elastic and inelastic electron scattering, surface and bulk, as well as extrinsic and intrinsic excitations can be regarded as independent processes and their contributions to the photoexcited electron spectra can be separated. While for low electron energies (e.g., below 500 eV) these assumptions may be partially valid only, increasing the electron energy (e.g., in the range of 5–10 keV), the role of elastic electron scattering, surface excitations and interference phenomena will be reduced significantly, as demonstrated above. The reviews of Tougaard [83] and Werner [31] in this Special Topical Volume provide more details on these (the QUASES [84] and the Partial

Intensity Analysis—PIA [41]) models for quantitative spectral interpretations and their applications. The parameters characterizing electron transport and utilized in spectrum simulation models can be derived from optical data [41] or from the analysis of spectra of quasi-elastically (using the EPES method [85]) and inelastically (using the bivariate reversion of REELS spectra method [31,86] or the QUEELS method and software [83,87] for deriving electron transport parameters or optical data – the dielectric function – from analysis of REELS spectra) backscattered electrons. The semiclassical – dielectric response – XPS model of Yubero and Tougaard [75,79] and the software based on this model [88] are applicable for simulating effects of core hole induced single intrinsic excitations and in addition to single bulk, single surface excitations as well, without assuming the independence of the different types of excitations. Simulation of wide range XPS and photon-induced Auger spectra of complex (e.g., layered) systems is possible using the SESSA software [89,31] that is based on the PIA approach as well as on an expert system for retrieving the parameters necessary for spectrum simulation from a comprehensive database. The validity of strong simplifying assumptions in modeling HAXPES spectra allows one to successfully apply procedures for describing the inelastic part of XPS spectra excited from solids in a way that is considerably simpler than those mentioned above. Such a model is the Extended Hüfner model [90–92], an improved version of the model proposed by Steiner, Höchst and Hüfner [93,94] accounting for spectral contributions from electrons suffering multiple energy losses of different origin, including even energy losses due to surface excitations and assuming the independence of the different types of excitations. The Extended Hüfner model (EH) proposes the following expression for describing the intensity distribution of the model photoelectron spectra [90]: Ymodel = A0 + A0 ⊗ Lb b + A0 ⊗ Lb a +

∞ 



(n−1) A0 ⊗ Lb

n=2

+

∞  z=1

(z−1)

A0 ⊗ Ls

cz z!

bn + n!

+

n−1  i=1

b(n−i) + an ai + (n − i)!

∞ ∞   n=1 z=1

(z−1)

An ⊗ Ls

cz +B z!

(17)

where Ymodel is the generated model spectral function, A0 is the photopeak (it can often be represented by a Doniach–Sunjic function [95] convolved by the spectrometer response function, usually represented by a Gaussian), ⊗ denotes convolution, Lb and Ls are the normalized DIIMFP and DSEP, n is the order of the bulk plasmon component, z the order of the surface plasmon component, An the nth complete bulk plasmon component, a the excitation probability of a bulk extrinsic plasmon, b the excitation probability of a bulk intrinsic plasmon, c the excitation probability of a surface plasmon (SEP), B is the contribution from the background attributable to electrons originating from higher kinetic energy peaks and to Bremsstrahlung. For illustration of the power of this simple method, Fig. 14 shows a comparison of experimental and model Ge 2s photoelectron spectra excited using 4000 eV energy X-rays [90]. The model spectrum was obtained by using the normalized DIIMFP (assuming the same distribution for bulk extrinsic and intrinsic excitations) and DSEP retrieved from the experimental Ge REELS spectra applying the procedure described in Ref. [43] and fitting the experimental data to Eq. (17) [90], according to the Extended Hüfner model based on only three fitting parameters (a, b, and c). The surface intrinsic excitations were neglected and for the photopeak a Doniach–Sunjic lineshape was assumed [90]. A very good agreement was obtained between the values of these parameters derived using the EH model and the corresponding values (a = 0.91, b = 0.13, c = 0.052) provided by the PIA method [90].

L. Kövér / Journal of Electron Spectroscopy and Related Phenomena 178–179 (2010) 241–257

Fig. 14. Comparison of the experimental and model Ge 2s photoelectron spectra excited using 4000 eV energy photons [91]. The model spectra was obtained by using the normalized DIIMFP and DSEP retrieved from the experimental Ge REELS spectra applying the procedure described in Ref. [43] and fitting the experimental data to Eq. (17).

It is interesting to see the possibilities for deriving these parameters from first principles. Further examples comparing the MH and PIA models [90–92] confirm that the value of the a parameter can be approximated by the value of the first partial intensity obtainable from Monte Carlo simulation [41] of electron elastic scattering in the material. For a nearly isotropic initial angular distribution of photoelectrons (e.g., when the scattering angle is close to the magic angle in the case of XPS) emitted from a semi-infinite homogeneous solid, the nth reduced partial intensity (cn = Cn /C0 [41]) can be expressed as cn = n [96] reflecting an exponential path length distribution of the measured photoelectrons in the solid. is given by [41,96]: =1−

ω/2 1 + cos 



3(1 − ω)

(18)

where  is the polar angle of emission and ω the single scattering albedo. In this case, the EH model – without Monte Carlo simulation – should give approximately the same result as the PIA method [91]. The parameter c in the EH model corresponds to the SEP and can be taken from the literature or from electron backscattering experiments. The parameter b is related to the probability of intrinsic bulk plasmon excitation; in principle, its value can be calculated using the semi-classical XPS dielectric response theory of Yubero and Tougaard [75,79] or the full quantum mechanical model of Fujikawa [14] which includes interference effects as well. For simple metals, a rough estimate [97] is b = rs /6, where rs is the radius of the Wigner-Seitz sphere in units of Bohr radius, giving b ∼ 1/3 for Al, Si and Ge. Interference effects between intrinsic and extrinsic excitations can be approximately described by a velocity dependent weakening of the strength of the intrinsic excitation. The parameter b is replaced with b* = b − (e2 /)F, where the coupling constant (e2 /) ∼ (13.6 eV/E)1/2 can be treated as an expansion parameter and F is a slowly varying but model dependent function of the electron velocity  and its magnitude is about unity [72,97]. Biswas et al. [80] recently assumed the F function to be proportional to the product of the probabilities of intrinsic and extrinsic excitations. In the case of Al, for an electron energy of 1.5 keV, the weakening, i.e., the decrease of the value of b due to the interference is ∼0.1 [72], in good agreement with the results obtained for Ge using the EH model [90]. It is difficult to obtain information on the contribution of intrinsic plasmon excitation to the measured photoelectron spectra, however, using a grazing incidence photon beam for excitation of

251

Fig. 15. Comparison of the experimental Ge 2s photoelectron spectra excited by 4600 eV energy photons from a Ge (1 1 1) single crystal using the “normal emission” (line) and “grazing incidence” (dots) experimental geometry [99], to the contribution of intrinsic excitations predicted earlier for “normal emission” (dashed line)[92]. ˛ denotes the angle of the photon beam related to the surface plane of the sample.

high energy photoelectrons, the contribution from extrinsic excitations to the spectra can be suppressed significantly due to the small depth of the layer from which the photoelectrons are emitted compared to the increased mean free path for inelastic electron scattering. In Fig. 15 [98] Ge 2s photoelectron spectra excited by 4600 eV energy photons from a Ge (1 1 1) single crystal using the “normal emission” and “grazing photon incidence” experimental geometry (where the angle of the photon beam is 45◦ and ca. 0.3◦ , respectively, compared to the surface plane) are compared to the contribution of intrinsic excitations predicted earlier for “normal emission”. A very significant decrease of the inelastic background can be observed in the case of the “grazing incidence” spectrum due to the suppression of the extrinsic excitations. However the intensity of the intrinsic loss contribution predicted by the simple EH model is still much lower than that of the spectrum taken at grazing photon incidence. A possible explanation for the large difference might be connected with the smaller role of the interference between the intrinsic and extrinsic excitations in the case of the spectrum taken using the grazing incidence photon beam. Due to the increase of the inelastic mean free path, by increasing the photon energy, a further decrease of the contribution from extrinsic losses can be seen [98]. Hard X-rays (even Bremsstrahlung radiation) are useful for exciting Auger transitions involving deep core levels, e.g., in the case of 3d elemental solids and these high energy Auger spectra can provide important information on the nature of the respective Auger processes in a solid environment – if measured using high energy resolution –, including information on the electronic structure in the proximity of the photon induced initial state core hole. These transitions are of a great practical importance since they are suitable for non-destructive chemical state resolved analysis of components at deeply buried interfaces. In addition, in the case of semiconductors used as charged particle or photon detectors, the precise knowledge of the respective deep core Auger spectra is important for understanding the response of the detectors, e.g., to X-rays. Fig. 16a shows high energy resolution Ge KL23 L23 Auger spectra excited from a thin polycrystalline Ge film using Bremsstrahlung radiation [99]. Applying two different models (QUASES-REELS [84] and PIA [41]) for estimating the contribution of electrons suffered inelastic scattering in the sample, the inelastic background was removed from the spectra [99]. The corresponding background-corrected spectra in Fig. 16a are similar, showing the presence of an intense satellite structure (p1) attributable to intrinsic plasmons induced by the suddenly appear-

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Fig. 17. Ni KLL Auger spectra photoexcited from a thick polycrystalline Ni sample (solid line) and from a Ni nanolayer deposited in situ onto a glassy carbon substrate (dashed line), using non-resonant conditions (photon energy above the K-shell ionization threshold) [102].

Fig. 16. (a) Comparison of the Ge KL23 L23 spectra obtained following the correction for inelastic background using the QUASES lineshape analysis [84] based on the REELS cross-section for inelastic electron scattering (dashed line) and the Partial Intensity Analysis [41] (solid line), respectively [99]. (b) The KLM Auger spectrum photoexcited from a thick polycrystalline Ni film, corrected for inelastic background using the PIA method (dots), together with the component peaks and the result of the fit (solid lines) [100].

ing core hole(s). Accounting for this plasmon structure, the relative transition energies and relative Auger peak intensities determined from the background-corrected spectra are in good agreement with relativistic atomic calculations and previous experiments [99]. Fig. 16b shows the first experimental high energy resolution KLM Auger spectrum photoexcited from a thick polycrystalline Ni film, following the correction of the inelastic background using the PIA method (dots), together with the component peaks and the result of the fit (solid lines) [100]. It should be noted that in order to avoid the appearance of interfering intense photoelectron peaks in the spectrum, the energy of the exciting photons has to be selected carefully, preferably using tunable synchrotron radiation for photoexcitation. This property of synchrotron radiation makes possible the measurement of deep core Auger spectra at a resonant condition, providing unique information on local electronic structure and dynamics of atomic excitations [101,27]. The determined relative Ni KLM Auger transition energies and line intensities show good agreement with the relativistic atomic calculations performed using the intermediate angular momentum coupling scheme [100]. The advent of the highly intense photon beams from advanced synchrotrons is obvious in HAXPES measurements, considering the low photoionization cross-sections. However, in the case of thick samples, the characteristic X-rays emitted within the solid following the core photoionization process, induce “internal” secondary photoionization and photoelectrons. Fig. 17 shows the high energy

resolution Ni KLL Auger spectra photoexcited from a thick polycrystalline Ni sample and from a less than 1 nm thick Ni nanolayer deposited in situ onto a glassy carbon substrate using non-resonant conditions (photon energy well above the K-shell ionization threshold) and grazing photon incidence in the case of the nanolayer [102]. The dramatic effect of the reduction of the inelastic background in the case of the nanofilm can be observed clearly. In addition, the photoelectron peaks excited by the characteristic Xrays photoinduced internally in the sample, can be clearly identified in the Auger spectrum of the thick sample, these peaks are absent in the case of the spectrum of the nanolayer. Fig. 18 illustrates the advantage of HAXPES for revealing bulk electronic structure from valence band photoelectron spectra. The figure shows experimental valence band XPS spectra photoexcited from a Fe (0 0 1) single crystal sample, using 0.2 keV (red circles) and 6 keV (black filled diamonds) energy photons, in comparison with theoretical calculations (red lines), indicating the contributions from the s (green dashed line), p (blue continuous line) and d (black dotted line) partial DOS components weighted by the corresponding relative photoionization cross-sections [103]. From these results, it is obvious that using 0.2 keV energy photons, the measured valence band photoelectron spectrum reflects practically the partial density of the d electronic states, at the same time contributions from the s and p partial density of states are greatly suppressed. Using 6 keV energy photons for excitation, the situation is reversed, the d DOS is suppressed and the contributions from the s and p DOS components determine the shape of the VB photoelectron spectrum [103]. 4. Applications of hard X-ray photoelectron spectroscopy Some examples will be now given of recent applications of HAXPES. One of the most important applications of HAXPES concerns extraction of information on bulk electronic structure of complex materials of high scientific or practical importance from high energy photon-induced (core and valence band) electron spectra. Recent developments of synchrotron radiation sources, monochromators and electron spectrometers, as well as the development of advanced methods for modeling spectral contributions from electron transport and excitations within the solids, have made it possible to derive accurate information on spectral features related to properties of bulk electronic structure. In Fig. 19 the valence

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253

Fig. 20. Comparison of the contributions of surface and bulk electronic states to the Ba 4d photoelectron spectra of the high TC superconductor YBa2 Cu3 Ox (x = 6.75) excited using different energy (given in eV) photons in the hard X-ray regime and different angles of emissions for the photoelectrons (NE = “normal emission”, in the direction of the surface normal of the sample) [105]. S and B indicate contributions from surface and bulk states, respectively.

Fig. 18. The experimental valence band XPS spectra photoexcited from a Fe (0 0 1) single crystal sample using 0.2 keV (red circles) and 6 keV (black filled squares) energy photons, compared with theoretical calculations (red lines), indicating the contributions from the s (green dashed line), p (blue continuous line) and d (black dotted line) partial DOS components weighted by the corresponding relative photoionization cross-sections [103]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

band photoelectron spectra of PrRu4 P12 (a Pr based filled skutterudite exhibiting an exotic metal–insulator transition and having the nature of the heavy fermion as a consequence of the hybridization between conduction and Pr 4f electrons) excited by 8175 eV and 825 eV energy photons is shown [104]. Although the energy resolution was around 100 meV for both the hard and the soft X-ray excitations [104], the hump structure close to the Fermi energy can

be observed only in the HAXPES spectrum. The small energy shift of the hump compared to the (P 3p partial DOS dominant) similar structure in the calculation is due to the recoil of the P atoms emitting the high energy photoelectrons [104]. HAXPES is often and successfully used for revealing fine details of the electronic structure of high TC superconductors. In Fig. 20 the contributions of surface and bulk electronic states to the Ba 4d photoelectron spectra of the high TC superconductor YBa2 Cu3 Ox (x = 6.75) are compared using different energy photon excitations and different experimental geometries [105]. As can be seen from the figure, in order to suppress the spectral contributions from the surface states significantly, it is necessary to use photon energy of at least 6 keV and normal emission geometry [105]. The charge transfer (an important physical quantity decisive for alloy stability) between components of binary alloys can be determined from analysis of alloy–metal Auger parameter shifts derived from experimental electron spectra photoinduced by hard X-rays [106–108], even in the case of very small charges transferred from one component to the other. Alloy–metal Auger parameter shifts can be obtained from measured alloy–metal shifts of the respective Auger electron kinetic energies and the respective electron binding energies monitored by the photoelectron peaks. Using the definition of Williams and Lang [109], the energy shift of the (“final state”) Auger parameter (j) is given by: (j) = Ek (ijj) − Eb (i) + 2 Eb (j)

where Ek (ijj) is the environmentally induced shift in the kinetic energy of an Auger transition involving the i and j core levels and Eb is the difference between the binding energy of a core level electron in the atom surrounded by two different (i.e., alloy and metal) atomic environments. If Eb is similar for all core levels, = ˛ = 2 Rea , where ˛ is the energy shift of the Auger parameter according to the conventional definition and Rea the environmentally induced change in the final state extra-atomic relaxation energy. For estimating charge transfer from experimentally derived final state Auger parameter shifts between a binary alloy and pure metals on the basis of a simple atomic structure model, can be shown [106]:

  dk  

= q

Fig. 19. Valence band photoelectron spectra of PrRu4 P12 excited by 8175 eV and 825 eV energy photons [104]. The solid line and open circles indicates the spectra measured below and above the metal–insulator transition temperature. The Ru 4d and P 3p partial density of electronic states obtained from band structure calculations are also indicated [104].

(19)

dN

+ k−2

 dk   dq   dU  dN

dN

+

dN

(20)

where q is the valence charge, k is the change in the core potential removing a valence electron, N is the occupation number of the core orbitals and U is the potential due to the surroundings. It is assumed that k and q depend linearly on N. An efficient on site screening of the core hole leads to (dU/dN) = (dq/dN) = 0, giving = q(dk/dN) when the valence electrons belong to a single band. The parameter dk/dN can be derived from atomic structure calculations. For the case of Au–Cu alloys, Table 3 contains the

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Table 3 Au–Cu Auger parameter shifts ˛ (eV) and transferred charges q [110]. Au3 Cu †

˛(Au) ˛(Cu) q(Au) q(Cu)

Table 4 Determined Ni overlayer thickness (nm) [118].

AuCu3

−0.01

Sample

0.24 −0.48 *

0.00(−0.03 ) −0.04+

−0.14

Ni 10 (as received) Ni 10 Ni 20 Ni 40 Ni 60

−0.11(−0.09 ) −0.12 *

−0.12+ 0.10(0.00* )

0.03(0.04* )

+

Ref. [111], from Mössbauer and XPS data. ˛ = q(dk /dN). dk /dN (Au): −2.2 [106]. dk /dN (Cu): −4.8 [114]. † Core average est. err.: |0.10| eV. * Derived on the basis of charge conservation: − qAu xAu = − qCu (1 − xAu ); x: atomic concentration.

experimental alloy-pure metal Auger parameter shifts (obtained from the high energy resolution Cu KLL and Au MNN Auger and Cu 2p, Au 3d, 4f photoelectron spectra of the respective alloy and pure metal samples) and the transferred charges derived using a linear potential model [110]. From the data presented in Table 3, it can be seen that for the AuCu3 alloy the derived charges are consistent with charge conservation and are in a very good agreement with previous XPS and Mössbauer spectroscopy studies [111] that predict a small, 0.1 e, overall charge transfer to the Au site. Charge transfer in the same direction is much smaller (∼0.03 e) in the case of the Au3 Cu alloy [110]. The observed tendency in the Cu and Au core level shifts [112] is confirmed by recent experiments [113]. Laboratory HAXPES equipment based on a monochromated Cu K␣ X-ray source was used, e.g., for Auger parameter shift measurements and charge transfer studies for Cr–Si alloys [3] and stainless steels [115]. In the analysis of Auger parameter shifts, the contributions to core level binding energy shifts from initial and final state effects can be separated. In the case of the SiO2 /Si (1 0 0) system Eickhoff et al. [116] studied Si 1s and 2p photoemission and Si KLL Auger emission using 3000 eV energy photons as a function of the thickness (0.4–3.8 nm) of the oxide overlayer. They found that the energy of the electrons photoinduced from the overlayers depended on the layer thickness. Using a generalized Auger parameter concept, the initial and final state contributions to the binding energy of the 2p electrons of the oxidized Si (Si4+ ) were separated and the initial state shift was found to be independent of layer thickness up to 2 nm [116]. An important application of HAXPES measurements is the determination of effective attenuation lengths (EALs) of electrons in different solids in the electron energy range 2–15 keV. However, the available experimental data in this energy region is rather scarce. Using the overlayer method and tunable energy synchrotron radiation (i.e., measuring photoelectron spectra excited from an overlayer of known thickness and from the substrate material with photons of different energies) the effective attenuation lengths for 4–6 keV energy electrons in Co, Cu, Ge and in Gd2 O3 were measured by Sacchi et al. [67]. Zemek et al. [66] applied the overlayer method to determine the effective attenuation lengths in Ni up to 2.1 keV electron energy using a laboratory XPS instrument. Rubio-Zuazo and Castro [117] used the overlayer method and synchrotron radiation to determine the information depth (based on their experimental EAL) in Au for photoelectrons with kinetic energies up to 15 keV. They found an information depth of 57 nm (99.8% of the detected photoelectrons originated within this depth) for an electron energy of 15 keV. From analysis of shapes of Auger and photoelectron spectra induced by hard X-rays from thin film overlayers the thickness of thin films can be determined. Table 4 [118] shows a comparison of the thicknesses (10–40 nm) of Ni films deposited in vacuum onto Si wafers and determined using different independent methods: (i)

a

Quartz crystal microbalance 10.5 10.5 20.6 40.8 60.7

XTEM

– 9.6 18.8 37.3 55.5

QUASESa KLL

Si 1s

10.8 10.6 20.8 39.0 Ref.

Ref. 8.3 18.3 – –

Ni KLL: Ni (6.5 keV) = 6.25 nm and Si 1s: Ni (6.2 keV) = 6.00 nm [85].

quartz crystal microbalance, (ii) cross-sectional transmission electron microscopy (XTEM), and (iii) spectral shape analysis using the QUASES method and software [84] with the recommended IMFPs taken from Ref. [85]. The good agreement among the film thicknesses given in Table 4 obtained using these different methods demonstrates the achievable accuracy of the spectral shape analysis method in the case of high energy Auger and photoelectron spectra excited from overlayer films of several tens of nm thickness [118]. One of the most interesting opportunities HAXPES is the nondestructive chemical analysis of buried layers, nanostructures and interfaces (lying at several times 10 nm depths from the surface of the solid). Fig. 21 [7] shows Si 1s photoelectron spectra excited – using 7935 eV energy photons – from NiGe/SiO2 (12 nm)/Si (1 0 0) structures with various thicknesses of the covering NiGe layer that confirm the feasibility of such analyses of deeply buried layers. As can be seen from Fig. 21, the peak attributable to Si 1s photoelectrons excited from the buried SiO2 layer can be clearly identified in the spectrum even for a 15 nm thick NiGe overlayer, while the Si 1s substrate peak is clearly observable in the same spectrum in spite of a 27 nm overlayer [7]. In other recent work [117] a 5 nm thick ı layer of La0.7 Ca0.3 MnO3 buried by a 53 nm thick layer of SrTiO3 was studied observing the La 3p3/2 peak (excited from the buried layer) in the photoelectron spectrum when tuning the photon energy to excite 12 keV energy La 3p3/2 photoelectrons. Since the escape depth of photoelectrons depends on their kinetic energy, using tunable energy photons (e.g., synchrotron radiation), XPS spectra from different depths – carrying nondestructively obtainable information on the chemical state resolved in-depth concentration distribution of the components of the surface/interface layers of solids – can be measured. Thin Ge (2 and 4 nm thick) layers deposited in vacuum onto the surface of a Si (1 0 0) substrate and after different treatments the surface and interface layers of the samples were analyzed by variable energy (1800–3700 eV) photon excited HAXPES [119], to obtain the depth profile of the Ge thin films and the buried interface layers. Depthdependent HAXPES measurements of Cu-depleted surface layer Cu(In,Ga)Se2 (the absorber material of thin film solar cells) films were performed varying the energy of the exciting photons in the

Fig. 21. Hard X-ray (using 7935 eV photon energy) excited Si 1s photoelectron spectra of a NiGe/SiO2 (12 nm)/Si (1 0 0) sample with varying NiGe overlayer thicknesses [7]. TOA indicates the take-off angle of photoelectrons, i.e., the angle of emission related to the surface of the sample.

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5. Summary and outlook

Fig. 22. Ti 2p photoelectron spectra excited from a LaAlO3 (LAO) on TiO2 -terminated SrTiO3 (STO) heterostructure as a function of the angle  of photoemission related to the surface normal (NE) of the sample [121].

range of 2–7 keV [120]. Good agreement was found between the experimental surface Cu content and the surface reconstruction model. The last example is concerned with angularly resolved HAXPES (AR-HAXPES) measurements. Because of the significantly increased IMFPs (and therefore the reduced depth resolution) when using hard X-rays for exciting photoelectron spectra, it might be thought, that AR-HAXPES measurements would not be useful. There are cases, however, when AR-HAXPES can provide unique and very important information. In Fig. 22 Ti 2p photoelectron spectra (recorded at room temperature) excited from a LaAlO3 (LAO) on TiO2 -terminated SrTiO3 (STO) heterostructure are shown as a function of angle of emission with respect to the surface normal of the sample [121]. From the low intensity peak at the position of the Ti 2p3/2 (Ti3+ ) line (not observable by soft X-ray photoelectron spectroscopy due to the smaller information depth) the authors identified the presence of additional electrons in the (otherwise empty) 3d shell of Ti4+ in STO. At larger emission angles – where the depth of origin of the signal photoelectrons decreases – the intensity of the Ti3+ spectral contribution increases compared to that of the main (Ti4+ ) photoelectron peak, indicating that the additional electrons are localized in an interface layer (with a thickness smaller than the escape depth of the electrons) between the LAO and the STO, close to the STO side [121]. From the results of these measurements, it was found that the two dimension interface electron gas was confined to at most a few STO unit cells [121]. The results support recent interpretations of the nature of the superconducting ground state of these structures [121].

With the recent developments in instrumentation (especially concerning the latest generation of synchrotron radiation sources and electron spectrometers) as well as in the theoretical description of high energy electron spectra, hard X-ray photoelectron spectroscopy of solids has reached maturity and has become an indispensable tool for many applications of great scientific or analytical importance. HAXPES is capable of providing information on bulk and interface electronic structure and chemical composition, even in the case of interface layers buried at several tens of nm depths. By tuning the energy of the exciting photon beam, chemical state resolved concentration depth profiling of the components becomes possible. Simple models for quantitative analysis may work quite well due to smaller elastic electron scattering effects. At grazing incidence photon excitation, surface effects can be amplified. However, special care is needed in both setting the conditions for high energy resolution experiments as well as in interpreting the experimental spectra, due to the low subshell photoionization cross-sections and the strong non-dipole effects in photoionization. For low atomic number components atomic recoil effects may limit energy resolution and make chemical state identification more difficult. Although several laboratory instruments exist already, the full capability of HAXPES can be exploited only at the latest generation synchrotron radiation sources. High energy and high energy resolution electron backscattering experiments are useful for extracting physical parameters and quantities characterizing scattering of high energy electrons in solids. These parameters and quantities (e.g., IMFP, SEP, DIIMFP, DSEP) are needed for interpretation/modeling of HAXPES spectra. Further studies are necessary to clarify the role and energy dependence of intrinsic excitations and interference effects. The significance of the AR-HAXPES applications are expected to increase in the future and a very interesting and promising prospect is the use of hard X-ray photoelectron diffraction for locating lattice distortions and determining impurity sites [122]. Another promising future direction concerns the possibility of a hard X-ray photoelectron emission microscope to provide images from deeply buried interface structures with very high lateral resolution [123]. Acknowledgements The author is indebted to Dr. C.J. Powell for his valuable comments. The financial support of the Hungarian grant OTKA K 67873 and of the DESY/HASYLAB and the European Community under Contract RII3-CT-2004-506008 (IASFS) is gratefully acknowledged. References [1] E. Sokolowski, C. Nordling, K. Siegbahn, Phys. Rev. 110 (1958) 776. [2] I. Lindau, P. Pianetta, S. Doniach, W.E. Spicer, Nature 250 (1974) 214. [3] G. Beamson, S.R. Haines, N. Moslemzadeh, P. Tsakiropoulos, J.F. Watts, P. Weightman, K. Williams, J. Electron Spectrosc. Relat. Phenom. 142 (2005) 151, and references therein. [4] L. Kövér, Zs. Kovács, J. Tóth, I. Cserny, D. Varga, P. Weightman, S. Thurgate, Surf. Sci. 433–435 (1999) 833. [5] H. Ishii, S. Mamaishin, K. Tamura, W.-G. Chu, M. Owari, M. Doi, K. Tsukamoto, S. Takahashi, H. Iwai, K. Watanabe, H. Kobayashi, Y. Kita, H. Yamazui, M. Taguchi, R. Shimizu, Y. Nihei, Surf. Interface Anal. 37 (2005) 211. [6] C.S. Fadley, Nucl. Instrum. Methods Phys. Res. A547 (2005) 24. [7] K. Kobayashi, Nucl. Instrum. Methods Phys. Res. A601 (2008) 32. [8] (a) C.S. Fadley, Nucl. Instrum. Methods Phys. Res. A 601 (2009) 8.; (b) C.S. Fadley, this volume. [9] D.P. Woodruff, this volume. [10] J. Zegenhagen, this volume. [11] (a) M.B. Trzhaskovskaya, V.I. Nefedov, V.G. Yarzhemsky, Atom. Data Nucl. Data Tables 77 (2001) 97; (b) M.B. Trzhaskovskaya, V.I. Nefedov, V.G. Yarzhemsky, Atom. Data Nucl. Data Tables 82 (2002) 257;

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