An analysis of the coincidence L2–L3M4,5 Coster–Kronig preceded Auger decay spectra of Fe and Co and the related Auger–Auger electron coincidence spectroscopy (AACS) spectra

Journal of Electron Spectroscopy and Related Phenomena 171 (2009) 1–17

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An analysis of the coincidence L2 –L3 M4,5 Coster–Kronig preceded Auger decay spectra of Fe and Co and the related Auger–Auger electron coincidence spectroscopy (AACS) spectra Masahide Ohno Quantum Science Research, 2–8–5 Tokiwadai, Itabashi-ku, Tokyo 174–0071, Japan

a r t i c l e

i n f o

Article history: Received 17 August 2007 Received in revised form 20 October 2008 Accepted 23 October 2008 Available online 12 November 2008 Keywords: Auger-photoelectron coincidence spectroscopy (APECS) Auger–Auger electron coincidence spectroscopy (AACS) Auger electron spectroscopy (AES) Photoelectron spectroscopy (PES) Coster–Kronig (CK) transition Auger transition Fe Co MnO Delocalization A many-body theory Auger cascade decay Auger-electron emitter

a b s t r a c t It is shown by a many-body theory that when the delocalization time of the M4,5 hole created in Fe (or Co) by the L2 –L3 V (V = M4,5 ) Coster–Kronig (CK) decay is much shorter than the L3 -hole lifetime, the coincidence (or singles (noncoincidence)) L2 –L3 V–L3 –VV Auger electron spectroscopy (AES) main line of Fe (or Co) coincides in line shape and peak KE with the intrinsic singles L3 –VV one. This is also the case with the Auger decay following the L1 –L2,3 V CK decay or the L1 V (or L2,3 V) shakeup/off excitations. Thus, there is no line shape change with photon energy in the singles L3 –VV AES main line of Fe (or Co). In the light of the delocalization of the M4,5 hole we analyzed the experimental singles and coincidence L2,3 –VV AES spectra of Fe and Co. The L3 photoelectron background intensity beneath the singles L2 photoelectron spectroscopy (PES) main line is found to be as large as the intrinsic singles L2 PES main line one. The relative intensity of the coincidence CK preceded AES spectrum to the coincidence L2 –VV one of Fe increases by a factor of about 2.7 because of the Auger electrons collected in coincidence with the L3 photoelectrons in the background beneath the singles L2 PES main line. A subtraction of the background appropriate respectively for the coincidence AES (or PES) spectrum and the singles one is necessary to compare the two spectra. We discussed the prospect of determining by Auger–Auger electron coincidence spectroscopy (AACS) the charge transfer (CT) screening time or the delocalization time of the valence-hole in a doubly ionized state using as an internal clock the lifetime of a core hole in the same doubly ionized state. We analyzed the Mn M2,3 V–VVV and Mn M2,3 M2,3 –VVVV AACS spectra of MnO. The present analysis of the Mn M2,3 V–VVV AACS spectrum of MnO measured in coincidence with the singles Mn L3 –M2,3 V AES peak shows that the delocalization time of the valence hole in the doubly ionized state in MnO is shorter than the L2,3 -hole lifetime but longer than the M2,3 one. © 2008 Elsevier B.V. All rights reserved.

1. Introduction Except for a very weak Auger satellite, there is not any appreciable line shape change between the singles (noncoincidence) L3 –VV (V = M4,5 ) Auger electron spectroscopy (AES) spectrum of Fe (or Co) metal measured just above the L3 -level ionization edge and the one far above the L1 -level ionization edge [1–4]. The Auger satellite is attributed to the L2 –L3 V–VVV Coster–Kronig (CK) preceded Auger decay [1,2]. The singles L3 –VV:L2 –VV AES spectral intensity ratio (6.7 [1]) significantly greater than two, the value expected from the electron populations in the initial states, shows the presence of CK decay [1,2]. The presence of CK decay and the nearly absence of Auger satellite in Fe (or Co) can be reconciled, if the M4,5 hole created by the CK decay hops away from the ionized atomic site and becomes screened out prior to the L3 -hole decay (Fig. 1) [1,2]. The authors of Refs. [1–4] did not realize that the M4,5 hole created either by the L2,3 (or L1 ) shakeup/off or by the L1 –L2,3 V CK 0368-2048/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2008.10.006

decay should also hop away prior to the L2,3 (or L1 )-hole decay (Figs. 2 and 3). Otherwise, the singles L2,3 –VV AES spectral line shape should vary with photon excitation energy. By varying photon excitation energy we open or close certain decay channel(s). However, in general with an increase in photon excitation energy the number of decay channels contributing to the singles AES spectrum increases so that an analysis of variation with photon energy in the singles AES spectral profile becomes more difficult. Moreover, the near ionization threshold excitation may result not only in the post collision interaction (PCI) effect on the singles AES spectral profile but also in a substantial variation with photon energy in the photoionization cross section. Thus, it would be more beneficial to be able to study the correlations between the initial events (photoemission) and the final ones (Auger electron emission) at a fixed photon excitation energy. By Auger-photoelectron coincidence spectroscopy (APECS) we collect in time coincidence a pair of a photoelectron and an Auger electron

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M. Ohno / Journal of Electron Spectroscopy and Related Phenomena 171 (2009) 1–17

Fig. 1. A schematic picture of the (CK preceded) Auger decay. Part (A) is the L3 –VV Auger decay. Part (B) is the L2 –L3 V–VVV CK preceded Auger decay. Part (C) is the L2 –L3 V–L3 –VV CK preceded Auger decay. For the sake of simplicity the localization of the valence-hole(s) in the L3 V and VVV states is not shown.

generated respectively by creation and annihilation of the same intermediate core–hole state. Thus, only features characteristic of that event contribute to the APECS spectrum. By explicitly exploiting this unique capability APECS enables photoemission and Auger electron emission of the same intermediate core–hole state, to be examined with unprecedented discrimination. As a part of a unified many-body theory of photoionization and core–hole decay, a basic theory of APECS by which major unique spectral features of APECS can be explained, was already formulated as early as in late 1970s [5]. The AES spectrum measured in coincidence with a selected singles photoelectron spectroscopy (PES) spectral peak kinetic energy (KE) is the partial singles AES spectrum modulated by spectral function R of a fixed energy elec-

Fig. 2. A schematic picture of the Auger decay. Part (A) is the L2,3 –VV Auger decay. Part (B) is the L2,3 V–VVV Auger decay of the L2,3 V satellite. Part (C) is the L2,3 V–L2,3 –VV Auger decay of the L2,3 V satellite. For the sake of simplicity the localization of the valence-hole(s) in the L2,3 V and VVV states is not shown.

tron analyzer which accepts photoelectrons of a selected KE. Here the partial singles AES spectrum is the singles one by Auger decay of the selected intermediate core–hole state. In the following we assume that the branching ratio of the partial Auger decay width to the lifetime width of the selected intermediate core–hole state is constant. When the selected KE of R coincides with the singles PES spectral peak KE, the modulation of the partial singles AES spectrum by R results in a symmetric line narrowing of the coincidence AES spectrum compared to the (partial) singles one. Otherwise, the modulation may result in an asymmetric line narrowing and a peak KE shift of the coincidence AES spectrum compared to the (partial) singles one. The line narrowing and peak KE shift depend on the FWHM of R. If R is a delta function, the broadening of the coincidence AES spectrum by the lifetime of the selected intermediate core–hole state can be eliminated and at the same time the peak KE shifts as much as the KE of E is varied within the singles PES peak, while if the FWHM of R is so large that R is photoelectron KE independent within the selected PES peak, i.e., the photoelectrons can be collected with an equal probability, the coincidence AES spectrum becomes identical to the partial singles one. However, in practice R is a Gaussian the FWHM of which is experimentally determined so that in principle the coincidence AES spectrum differs from the partial singles one. As the singles L2,3 –VV AES main line of Fe (or Co) does not vary in both line shape and peak KE with photon excitation energy, we expect that the CK preceded AES spectrum of Fe (or Co) measured in coincidence with the singles L2 PES peak resembles the L3 –VV AES spectrum measured in coincidence with the singles L3 PES peak, except for a weak CK preceded AES satellite in the former spectrum. The coincidence L2 –L3 V CK preceded AES spectrum of Fe is indeed very similar in line shape to the coincidence L3 –VV one, except for a large discrepancy in line shape in the lower KE tail and the former spectral peak shift by 0.8 ± 0.2 eV to higher KE compared to the latter one, whereas the former spectrum of Co narrows by as much as 37% compared to the latter one, and the former spectral peak is shifted by 1.1 ± 0.2 eV to lower KE compared to the latter one [6]. The authors of Ref. [6] attributed the coincidence L2 –L3 V CK preceded AES spectrum of Fe (or Co) to the L2 –L3 V–VVV (band like) spectator Auger decay so that the line narrowing and the peak KE shift of the coincidence CK preceded AES spectrum of Co compared to that of Fe is due to an increase in the Coulomb hole–hole repulsion energy in the Auger three-hole final state from Fe to Co by an increase in the additional Coulomb hole–hole repulsion energy by the presence of the spectator hole. Their interpretation contradicts much with the one in Refs. [1–4] that the M4,5 hole created in Fe (or Co) by the CK decay hops away rapidly prior to the L3 -hole decay so that the CK preceded Auger decay results in a two-hole state rather than a three-hole state. In the present paper we show by a many-body theory that when the delocalization time of the M4,5 hole created either by the CK decay or by the shakeup/off is much shorter than the L3 -hole decay time, the singles L2 –L3 V–L3 –VV CK preceded AES main line coincides in both line shape and peak KE with the intrinsic singles L3 –VV one so that the singles L3 –VV AES main line does not show any line shape change with photon energy. We show also by a many-body theory how the coincidence L2 –L3 V–L3 –VV (or L2 –L3 V–VVV) CK preceded AES main line (or satellite) and the coincidence L2,3 –VV AES spectrum should look compared to the correspondent singles one because the authors of Ref. [6] interpreted without any argument the coincidence AES spectra as the correspondent singles one. However, the coincidence AES spectrum is modulated by R so that the comparison of the coincidence AES spectrum with the correspondent singles one should be justified, in particular when the Auger cascade decay such as the CK preceded Auger decay is concerned. We then analyze the singles and coincidence AES spectra

M. Ohno / Journal of Electron Spectroscopy and Related Phenomena 171 (2009) 1–17

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Fig. 3. A schematic picture of the CK preceded Auger decay. Part (A) is the L1 –L2,3 V–VVV CK preceded Auger decay. Part (B) is the L1 –L2,3 V–L2,3 –VV CK preceded Auger decay. Part (C) is the L1 –L2 V–L3 VV–VVVV CK preceded Auger decay. Part (D) is the L1 –L2 V–L2 –L3 V–L3 –VV CK preceded Auger decay. Part (E) is the L1 V–L2 VV–L3 VVV–VVVVV CK preceded Auger decay of the L1 V satellite. Part (F) is the L1 V–L1 –L2 V–L2 –L3 V–L3 –VV CK preceded Auger decay of the L1 V satellite. For the sake of simplicity the localization of the valence-hole(s) in the doubly (and multiply) ionized state is not shown.

in Ref. [6] to determine the L3 -hole Auger decay width. We discuss a cause of the discrepancy in line shape and peak KE between the coincidence CK preceded AES spectrum and the coincidence L3 –VV one for Fe (or Co). Finally we discuss the prospect of determining

in general the screening time of a valence-hole in a doubly ionized state by collecting in time coincidence by Auger–Auger electron coincidence spectroscopy (AACS) a primary Auger electron and a secondary one generated respectively by creation and annihilation

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of the same doubly ionized state. As an example we discuss the Mn M2,3 V–VVV (or M2,3 M2,3 –VVVV) AACS spectra of MnO measured in coincidence with the Mn L3 –M2,3 V (or M2,3 M2,3 ) AES peak KE. 2. Singles and coincidence L2 –L3 V CK preceded Auger decay spectra 2.1. Coincidence L2 –L3 V CK preceded Auger decay spectrum We employ the unitary expansion method by which a one-step model of photoionization and core–hole decay was formulated in Ref. [5]. The doubly differential photoionization cross section of L2 -level photoemission and L2 –L3 V CK preceded Auger electron emission by which a photoelectron and an Auger electron, the KEs of which are ε and εA , respectively, are emitted, is given by the following (Fig. 4) d2  = dε dεA

 [

|Pε Gc (ε − ω)Vck (εck )Gc v (ε − ω − εd + εck )

f

× Vc f (εA )|2 d (εd )Df (ε − ω + εA + εck )dεck dεd ] +

 [

|Pε Gc (ε − ω)Vck (εck )Gc v (ε − ω − εd + εck )

f

× Vr Gc (˜ε − ω)Vc f (εA )|2 d (εd )Df (˜ε − ω+εA )d˜ε dεck dεd ] (1) The first term is due to the L2 –L3 V–VVV CK preceded Auger decay in which the M4,5 hole created by the CK decay remains at the ionized atomic site during the L3 -hole decay (Fig. 4(A)), while the second term is due to the L2 –L3 V–L3 –VV one in which the M4,5 hole created by the CK decay hops away from the ionized atomic site prior to the L3 -hole decay (Fig. 4(B)). Pε is the dipole transition matrix element of photoemission, ω the incident photon energy fixed far above the ionization threshold, the energy distribution of which is neglected for the sake of simplicity, Gc the L2 -hole propagator, Vck the L2 –L3 V CK decay matrix element, εck the CK–electron KE, Gc v the L3 V two-hole propagator, εd the M4,5 -hole energy, d the density of the M4,5 -hole states in the presence of the L3 hole, i.e., the density of the M4.5 -hole states renormalized by the Coulomb repulsion energy Ucd between the M4.5 hole and the L3 hole. When Ucd becomes larger than the M4,5 band width W, a bound M4,5 hole level appears below the band edge in the presence of L3 hole. For the sake of simplicity in such a case we neglect the multiplet of the L3 V states. Vc f is the L3 V–VVV spectator Auger decay matrix element, Df the density (or spectral function) of the three M4,5 -hole states renormalized by 3Uvv = 2Udd + Udd (d). Udd is the Coulomb repulsion energy between two M4.5 holes created in a neutral ground state, Udd (dn ) the one between two M4.5 holes created in the ionized state in which n M4,5 holes are already created, Uvv the one between two M4.5 holes in the three M4,5 -hole state. Note that Uvv is not equal to Udd . Gc is the L3 -hole propagator, Vr (the energy independent) relaxation matrix element connecting the L3 V state with the single L3 -hole state, Vc f the L3 –VV Auger decay matrix element, Df the density of the two M4,5 -hole states renormalized by Udd . The L2 photoelectron and the CK electron are generated respectively by creation and annihilation of the L2 -hole state. If the hopping time of the M4,5 hole in the L3 V state is much shorter than the L3 -hole lifetime in the presence of the M4,5 hole, the L3 V state relaxes to the L3 -hole state prior to the L3 -hole decay. The L2 photoelectron and the CK electron are then “decoupled” from the fully relaxed L3 -hole state and the subsequent L3 -hole Auger decay. We thus introduce a dummy energy ε˜ in the second term in Eq. (1) as the sum of the L2 photoelectron KE, the CK–electron KE

Fig. 4. Feynman diagrams of the CK preceded Auger decay. Part (A) is the L2 –L3 V–VVV CK preceded Auger decay. Part (B) is L2 –L3 V–L3 –VV CK preceded Auger decay.

and the relaxation energy so that the energy conservation law is respected. Using Eq. (1) we obtain the following L2 –L3 V–VVV AES satellite and the L2 –L3 V–L3 –VV AES main line measured in coincidence with the L2 photoelectrons of a selected KE (ε◦ ). d2  = dεA dε◦



|Pε |2 Ac (ε − ω)

f

× +

|Vc f (εA )|2 D (ε − ω+εA + εck )R(ε, εo )dεck dε c v (ε−ω + εck )+ f

  f



  (ε − ω) R(ε, εo )dε |Pε | Ac (ε−ω) ck c (ε − ω) c v +  2

 ×

|Vck (εck )|2 Ac v (ε − ω + εck ) c (ε − ω)



Ac (˜ε − ω)

|Vc f (εA )|2 D  (˜ε − ω + εA )d˜ε c (˜ε − ω) f

(2)

Ac is the L2 -hole spectral function,  c the L2 -hole lifetime width, Ac v the L3 M4,5 two-hole spectral function, i.e., the convolution of the imaginary part of Gc v with d divided by ,  the relaxation width defined by  = |Vr |2 , c v the L3 -hole lifetime width in the L3 M4,5 state,  CK the CK–decay width, Ac the L3 -hole spectral function,  c the L3 -hole lifetime width, R the spectral

M. Ohno / Journal of Electron Spectroscopy and Related Phenomena 171 (2009) 1–17

function of a fixed energy electron analyzer which accepts photoelectrons of a selected KE (ε◦ ). R is a Gaussian function the FWHM of which is experimentally determined. We introduced formally the imaginary part of the L2 (or L3 )-hole self-energy as the photoelectron–KE dependent lifetime width. However, the lifetime widths in Eq. (2) are photoelectron–KE independent because the Auger (or CK) decay width is independent of photoelectron KE in the L2,3 PES main line and satellite. For the sake of simplicity we do not introduce explicitly the spectral function of a fixed energy electron analyzer which accepts the Auger electrons of a selected KE. The first term is the coincidence L2 –L3 V–VVV AES satellite. It is the singles L3 V–VVV AES satellite weighted by the branching ratio of the CK decay width to the L2 -hole lifetime width, convoluted by the product of R and the singles L2 PES main line. Thus, when the selected L2 photoelectron KE coincides with the singles L2 PES peak KE, the coincidence L2 –L3 V–VVV AES satellite line shows a symmetric line narrowing compared to the singles one. Otherwise, the former line is asymmetrically narrowed and shifted compared to the latter one. The KE shift and line narrowing depend on the FWHM of R. Unless R is a delta function, the KE shift is not equal to that of R from the singles PES peak KE. We obtain the singles L2 –L3 V–VVV AES satellite by eliminating R in Eq. (2). The second term is the coincidence L2 –L3 V–L3 –VV AES main line. It is the product of the two quantities X and Y. X, the second squared brackets, is the intrinsic singles L3 –VV AES spectrum, i.e., the singles L3 –VV AES spectrum solely by the L3 –VV Auger decay of the L3 PES main line including the L3 –VVV Auger shakeup/off. Y, the first squared brackets, is the singles L2 PES main line weighted by the branching ratio of the CK decay width to the L2 -hole lifetime width and that of the relaxation width to the lifetime width of the L3 V state, convoluted by R. Y depends on R. However, X is independent of Y so that the coincidence L2 –L3 V–L3 –VV AES main line then coincides in line shape and peak KE with the intrinsic singles L3 –VV one. The line shape and peak KE are independent of R. It is clear that when the delocalization time of the valencehole in the L3 V state is much shorter than the L3 -hole lifetime, the second term in Eq. (2), namely the coincidence L2 –L3 V–L3 –VV AES main line, dominates in the coincidence CK preceded AES spectrum. 2.2. Singles L2 –L3 V CK preceded Auger decay spectrum To prove the validity of the present formalism we need to show that if the M4,5 hole created either by the CK decay or by the shakeup/off delocalizes prior to the L2,3 (or L1 )-hole decay, there is no line shape change and peak KE shift between the singles L3 –VV AES spectrum measured just above the L3 -level ionization edge and the one far above the L1 -level ionization edge. We eliminate R in the second term in Eq. (2) in order to obtain the singles L2 –L3 V–L3 –VV AES main line which dominates in the singles CK preceded AES spectrum, when the delocalization time of the valence-hole in the L3 V state is much shorter than the L3 hole lifetime. The singles L2 –L3 V–L3 –VV AES main line coincides in Line shape and peak KE with the intrinsic singles L3 –VV one. The L2 -hole lifetime does not broaden the singles L2 –L3 V–L3 –VV AES main line. Otherwise, the singles L2 –L3 V–L3 –VV AES main line becomes broader than the singles L3 –VV one so that the singles L3 –VV AES main-line shape varies with photon energy. However, the singles L3 –VV AES main line of Fe (or Co) does not show any line broadening with photon energy [1,2]. The authors of Refs. [1–4] did not realize the important point that the L2 -hole lifetime width does not contribute to the singles L2 –L3 V–L3 –VV AES main line of Fe (or Co), despite that the L2 -hole lifetime width (FWHM) of

5

Fe (or Co) is as large as 0.88 eV (or 1.16 eV) [7] so that it is not negligible. Above the L1 -level ionization edge the singles L2 (or L3 )–VV AES spectrum of Fe (or Co) does not show any line shape change compared to the one measured just above the L2 (or L3 )-level ionization edge [1,2]. The M4,5 hole created by the L1 –L2,3 V CK decay must then delocalize rapidly prior to the L2,3 -hole decay. If this is so, the present theory shows that the singles L1 –L2,3 V–L2,3 –VV AES main line coincides in line shape and peak KE with the intrinsic singles L2,3 –VV one and the singles L1 –L2 V–L2 –L3 V–L3 –VV one coincides in line shape and peak KE with the intrinsic singles L3 –VV one. The L1 -hole lifetime width of Fe or Co is as large as about 6 eV [8]. However, it does not contribute to the singles L1 –L2,3 V–L2,3 –VV and L1 –L2 V–L2 –L3 V–L3 –VV AES main line of Fe (or Co). Otherwise, the singles L2,3 –VV main-line shape of Fe (or Co) should vary appreciably with photon energy, although the contribution of the L1 -hole induced decay is small (see later). The L2.3 V (or L1 V) shakeup/off satellite relaxes to the L2,3 (or L1 )-hole state prior to the L2,3 (or L1 )-hole decay. The present theory shows that the singles L2,3 V–L2,3 –VV (or L2 V–L2 –L3 V–L3 –VV, L1 V–L1 –L2,3 V–L2,3 –VV or L1 V–L1 –L2 V–L2 –L3 V–L3 –VV) AES main line then coincides in line shape and peak KE with the intrinsic singles L2,3 –VV one. For an example we can describe the L2.3 V–VVV decay and the L2.3 V–L2,3 –VV one by making following changes in Eq. (1). We replace Gc by the L2,3 -hole propagator, Vck by the L2,3 shakeup/off matrix element,  c by the imaginary part of the L2,3 -hole self-energy including the L2,3 -hole shakeup/off self-energy, and Gc by the L2,3 -hole propagator. The present many-body theory shows that when the M4,5 hole created either by the shakeup/off or by the CK decay delocalizes rapidly prior to the core–hole decay, there is no line shape change and peak KE shift in the singles L3 –VV AES spectrum with photon energy. This is in accord with the experimental finding in Refs. [1–4]. 2.3. PCI The Auger-electron KE is high but the CK–electron KE is low in the CK preceded Auger decay final state. There could be PCI between a slow CK electron and a fast Auger electron irrespective of photoelectron KE. Near the L2 -level ionization edge there could be an additional PCI between a slow photoelectron and a slow CK electron (or a fast Auger electron). The singles CK preceded AES main line should then show line shape change compared to the intrinsic singles L3 –VV AES one measured in the sudden limit. However, the singles L3 –VV AES main line of Fe (or Co) does not show any line shape variation with photon energy. The PCI between a slow CK electron (or photoelectron) and a fast Auger electron is then absent irrespective of photon energy. This is because the photoelectron and the CK electron are decoupled from the Auger decay of the L3 -hole state via the relaxation of the L3 V state (Section 2.1). The PCI between a slow photoelectron and a slow CK electron in the CK final state prior to the delocalization of the M4,5 hole modulates only the first squared brackets in the second term in Eq. (2) so that it does not affect the line shape and peak KE of the singles L2 –L3 V–L3 –VV CK preceded AES main line. When the photon energy is near the L2,3 -level ionization edge, we expect the PCI between a slow photoelectron and a fast Auger electron in the L2,3 –VV Auger decay. However, the singles L2,3 –VV AES main line of Fe (or Co) does not show any line shape change with photon energy. The absence of PCI means that the change in the potential from the L2,3 -hole state to the Auger final state is very small. Because the two M4,5 holes created in Fe (or Co) by the Auger decay are delocalized in contrast to the localized case in which the PCI is observed.

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M. Ohno / Journal of Electron Spectroscopy and Related Phenomena 171 (2009) 1–17

3. Coincidence and singles AES spectra of Fe 3.1. Coincidence and singles L2,3 –VV AES spectra of Fe The L2,3 –VV Auger decay spectrum measured in coincidence with the L2,3 PES main line is given by the following. d2  = dεA dε◦



|Pε |2 Ac (ε − ω)R(ε, ε◦ )

f

×

|Vc f (εA )|2 D  (ε − ω + εA )dε c (ε − ω) f

(3)

The resolution width (FWHM = 2.6 eV) of R in Ref. [6] is 11 (or 6.5) times larger than the L3 -hole lifetime width (FWHM = 0.24 eV [7] or 0.4 eV (present work)) of Fe so that all photoelectrons in the L3 PES main line are collected with an approximately equal probability. We can then assume R in Eq. (3) to be independent of photoelectron KE so that the coincidence L3 –VV AES spectrum of Fe becomes identical to the intrinsic singles one solely by the L3 –VV Auger decay including the Auger shakeup/off. For the moment we leave out the inelastic Auger-electron background in the lower KE tail of the coincidence L3 –VV AES spectrum. If the delocalization time of the M4,5 hole created in Fe either by the L1 –L2,3 V (or L2 –L3 V) CK decay or by the L1 V (or L2,3 V) shakeup/off is longer than the L1 -hole lifetime and the L2,3 -hole one, the singles L3 –VV AES spectrum consists of the L3 –VV Auger decay and Auger satellite cascade decays listed in Table 1. However, the delocalization time of the M4,5 hole created in Fe either by the L1 –L2,3 V (or L2 –L3 V) CK decay or by the L1 V (or L2,3 V) shakeup/off is much shorter than the L1 -hole lifetime and the L2,3 -hole one, the singles L3 –VV AES spectrum then consists of the L3 –VV Auger decay and the Auger main line cascade decays listed in Table 1. The present theory shows that the singles C–C V–C –VV, C V–C –VV, C –CV–C–C V–C –VV, C V–C –C V–C –VV and C V–C –CV–C–C V–C –VV AES spectra coincide in line shape and peak KE with the intrinsic singles C –VV AES spectrum. The coincidence L3 –VV AES spectrum which is essentially identical to the intrinsic singles one should then coincide in line shape and peak KE with the singles one. The two spectra indeed coincide well in line shape except for a large discrepancy in the lower KE tail (Fig. 5). We refer to Ref. [9] for a calculation of the singles L3 –VV AES spectrum of Fe metal which is the self-fold of the DOS, perturbed by Udd . The resolution width of R in Ref. [6] is 3 (or 2.5) times larger than the L2 -hole lifetime width (FWHM = 0.88 eV [7] or 1.04 eV

Main line

Satellite

(present work)) of Fe. Thus, the coincidence L2 –VV AES spectrum still becomes the intrinsic singles one narrowed by R. The intrinsic singles L2 –VV AES spectrum is the singles one solely by the L2 –VV Auger decay including the Auger shakeup/off. If the delocalization time of the M4,5 hole created in Fe either by the L1 –L2 V CK decay or by the L1 V (or L2 V) shakeup/off is longer than the L1 -hole lifetime and the L2 -hole one, the singles L2 –VV AES spectrum consists of the L2 –VV Auger decay and Auger satellite cascade decays listed in Table 1. However, the delocalization time of the M4,5 hole created in Fe either by the L1 –L2 V CK decay or by the L1 V (or L2 V) shakeup/off is much shorter than the L1 -hole lifetime and the L2 -hole one. The singles L2 –VV AES spectrum then consists of the L2 –VV Auger decay and the Auger main-line cascade decays listed in Table 1. The singles L2 –VV AES spectrum thus coincides in line shape and peak KE with the intrinsic singles one. The coincidence L2 –VV AES spectrum of Fe which is the intrinsic singles L2 –VV AES spectrum narrowed by R is indeed narrower than the singles one (Fig. 5).

L1 –L2 V–L2 –VV L1 V–L1 –L2 V–L2 –VV L2 –VV L2 V–L2 –VV

L1 –L2 V–VVV L1 V–L2 VV–VVVV L2 V–VVV

3.2. Coincidence and singles L2 –L3 V CK preceded Auger decay spectra of Fe

Table 1 Decay channels contributing to the singles L2,3 –VV AES spectrum of Fe metal. Intrinsic singles L2 –VV

L2 –VV

Intrinsic singles L3 –VV

L3 –VV

Fig. 5. Line A is the singles L2,3 –VV AES spectrum of Fe [6]. Line B is the coincidence L3 –VV AES spectrum scaled for comparison with the singles one [6]. The present theory shows that the coincidence L3 –VV AES spectrum B should coincide in line shape and peak KE with the intrinsic singles one E. Line E is the intrinsic singles L3 –VV AES spectrum obtained by subtracting the inelastic Auger electron background from the coincidence one (Line B). The coincidence L3 –VV AES spectrum B coincides well in line shape and peak KE with the singles one A, except for the lower KE tail. Line C is the coincidence L2 –L3 V CK preceded AES spectrum and the coincidence L2 –VV one [6]. The present theory shows that the former spectrum should coincide in line shape and peak KE with the intrinsic singles L3 –VV AES spectrum E. Line D is the coincidence L2 –L3 V CK preceded AES spectrum C scaled for comparison with the singles L3 –VV one A. They coincide well in line shape except for a discrepancy in the lower KE tail and a peak KE shift of about 0.8 eV.

Singles L2 –VV

Singles L3 –VV Main line

Satellite

L1 –L2 V–L2 –L3 V–L3 –VV L1 V–L1 –L2 V–L2 –L3 V–L3 –VV L1 –L3 V–L3 –VV L1 V–L1 –L3 V–L3 –VV L2 –L3 V–L3 –VV L2 V–L2 –L3 V–L3 –VV L3 –VV L3 V–L3 –VV

L1 –L2 V–L3 VV–VVVV L1 V–L2 VV–L3 VVV–VVVVV L1 –L3 V–VVV L1 V–L3 VV–VVVV L2 –L3 V–VVV L2 V–L3 VV–VVVV L3 V–VVV

The delocalization time of the M4,5 hole created in Fe by the L2 –L3 V CK decay is much shorter than the L3 -hole decay time. The coincidence L2 –L3 V–L3 –VV AES spectrum of Fe then coincides in line shape and peak KE with the intrinsic singles (or singles) L3 –VV one (Eq. (2)). The former spectrum indeed coincides in line shape with the coincidence L3 –VV AES one, except for a discrepancy in the lower KE tail and a small peak KE shift (Fig. 5). The coincidence L3 –VV AES spectrum of Fe essentially coincides in line shape and peak KE with the intrinsic singles one (Section 3.1). The discrepancy in line shape in the lower KE tail and a small peak KE shift must then be due to the

M. Ohno / Journal of Electron Spectroscopy and Related Phenomena 171 (2009) 1–17

processes not considered in Eqs. (2) and (3). The coincidence CK preceded AES spectrum of Fe coincides in line shape with the singles L3 –VV one, except for a small peak KE shift (Fig. 5). The discrepancy in line shape in the lower KE tail between the singles L3 –VV AES spectrum and the coincidence one as well as that between the coincidence CK preceded AES spectrum and the coincidence L3 –VV one must be due to the processes not considered so far (see later). 3.3. Singles L2,3 –VV AES spectrum and Auger decay width of Fe The L2,3 -hole lifetime width of Fe was determined in Ref. [7] by the intensity ratio of the singles L3 –VV AES spectrum to the singles L2 –VV one. As the AES satellite intensity is very small in Fe, we obtain the following intensity ratio of the singles L3 –VV AES spectrum to the singles L2 –VV one (see Table 1 for a summary of decay channels).



˜= R

7

Table 2 L2 –L3 V CK decay width and Auger decay width of Fe metal (in eV). CK decay width

Auger decay width

Experiment

Experiment

Theory

0.64 [7]

0.24 [7] 0.40a

0.41 [14]

a

Present work or from the data in Ref. [1].

induced decay is small so that Eq. (5) becomes almost identical to Eq. (1) in Ref. [7]. 3.4. Inelastic and elastic Auger electron background When an Auger electron is collected in coincidence with a photoelectron experiencing a certain number of inelastic collisions, the

L1 (L1 −L3 V /L1 )(L3 −VV /L3 ) + L1 (L1 −L2 V /L1 )(CK /L2 )(L3 −VV /L3 ) + L2 (CK /L2 )(L3 −VV /L3 ) + L3 (L3 −VV /L3 ) L1 (L1 −L2 V /L1 )(L2 −VV /L2 ) + L2 (L2 −VV /L2 )

Here L1 the L1 -level photoionization cross section, L2 the L2 -level one, L3 the L3 -one,  x the (x = L1 or L2 or L3 )-hole lifetime width,  X–Y the X–Y, Auger decay width. Using the theoretical photoionization cross sections of the L1 , L2 and L3 levels of Fe [10] and the theoretical branching ratio of the L1 –L2 (or L3 )V CK decay width [11], we rewrite Eq. (4) as the following. ˜ = 2.965 R



CK + 1.965 L3

(5)

Eq. (5) is essentially the same as Eq. (1) in Ref. [7]. However, Eq. (1) in Ref. [7] was derived without taking into account the L1 -hole decay and the decay of the shakeup/off satellite. Eq. (5) is valid only when the M4,5 hole created either by the CK decay or by the shakeup/off delocalizes rapidly before the L1 (or L2 , L3 )-hole decays. Otherwise, we have to take explicitly into account the variation in the branching ratio of the Auger (or CK) decay width with a number of the spectator hole. We reported elsewhere such an approach employed for an analysis of the variations with photon energy in the singles L2,3 –VV AES (satellite/main line) spectral intensity ratios of Cu metal and CuO in which the M4,5 hole created either by the CK decay or by the shakeup/off remains localized during the L1 (or L2,3 )-hole decay [12,13]. For an analysis of the singles L2,3 –VV AES spectrum of Fe in Ref. [6] we pay attention to the followings; (i) the coincidence L3 –VV AES spectrum coincides in line shape and peak KE with the singles one, except for a lower KE tail (Fig. 5). We subtract the inelastic Auger electron background from the coincidence L3 –VV AES spectrum to obtain the intrinsic singles one (Fig. 5). (ii) The singles L2 –VV AES spectrum should coincide in line shape with the singles L3 –VV one, except for the extra former main-line broadening by the L2 –L3 V CK decay (0.64 eV [7]). In the light of (i) and (ii) we find that the intensity ratio of the singles L3 –VV AES peak to the singles L2 –VV one is 6.7. The ratio agrees with 6.7 (5∼10) reported in Ref. [1] (the ratio in Ref. [7] is 10). The ratio of the CK decay width to the L3 hole lifetime width is then 1.6 (Eq. (5)). The experimental L2 –L3 V CK decay width of Fe is 0.64 eV [7]. We then obtain 0.4 eV for the L3 -hole lifetime width of Fe. The L3 -hole lifetime width of atomic Fe calculated by an ab initio atomic independent-particle approximation is 0.41 eV [14]. The agreement with the L3 -hole lifetime width determined in the present work is excellent. The L2 -hole lifetime width of Fe which is the sum of the L3 -hole lifetime width and the CK decay width, is then 1.04 eV (Table 2). We determined by Eq. (4) the percentage contributions of the decay channels to the singles L2,3 –VV AES spectrum of Fe and summarized them in Table 3. The percentage contribution of the L1 -hole

(4)

probability for the Auger electron to experience also inelastic collisions increases because both of them are emitted by the same atom, although the probability depends on the KE [15]. The inelastic Auger electron background in an AES spectrum measured in coincidence with elastic photoelectrons in the main line is thus reduced compared to the one in a singles one measured irrespective of photoelectrons. This explains a decrease by about 40% in the relative inelastic Auger electron background intensity in the lower KE tail in the coincidence L3 –VV AES spectrum compared to that in the singles L3 –VV AES spectrum. The authors of Ref. [6] attributed the discrepancy in line shape between the coincidence L2 –L3 V CK preceded AES spectrum and the coincidence L3 –VV one to the CK preceded AES satellite. However, the AES satellite intensity is too small to explain the discrepancy. We attribute the discrepancy in line shape between the singles L3 –VV AES (or coincidence CK preceded AES) spectrum and the coincidence one to the inelastic Auger electrons correlated with the inelastic L3 photoelectrons. We neglect the very weak CK preceded AES satellite in Fe. We then integrate the second term in Eq. (2), and Eq. (3) over the Auger-electron KE to obtain the intensity ratio of the coincidence CK preceded AES main line to the coincidence L2 –VV one. The ratio is equal to that of the CK decay width to the Auger decay width. The Auger decay width is 0.4 eV (or 0.24 eV [7]). The ratio is then 1.6 (or 2.67). However, the ratio in Ref. [6] is 4.3 ± 0.6. The coincidence CK preceded AES spectrum must coincide in line shape and peak KE with the coincidence L3 –VV one. We obtain the ratio (4.3) by comparing the coincidence L2 –VV AES spectrum (without the inelastic Auger electron background) with the coincidence L3 –VV AES spectrum (without the inelastic Auger electron background) scaled to the coincidence CK preceded AES spectrum. The experimental ratio is too large. The fixed energy photoelectron analyzer set on the singles L2 PES main line picks up not only the inelastic L3 photoelectrons emitted by the L3 PES main line but also the Table 3 Percentage contributions to the singles L2,3 –VV AES main line of Fe metal. Singles L2 –VV main line L1 -hole induced decay

L2 -hole induced decay

8.1

91.9

Singles L3 –VV main line L1 -hole induced decay

L2 -hole induced decay

L3 -hole induced decay

9.0

21.9

69.1

8

M. Ohno / Journal of Electron Spectroscopy and Related Phenomena 171 (2009) 1–17

Table 4 Auger decay channels contributing to the coincidence L2 –L3 V CK preceded AES main line according to the photoelectrons collected in coincidence. Photoelectron Auger electron

L2 photoelectron L2 –L3 V–L3 –VV

L3 V satellite L3 V–L3 –VV

L3 photoelectron L3 (inelastic)–VV

Table 5 The intensity ratio of the L3 photoelectron background beneath the L2 PES main line to the intrinsic L2 PES main line in Fe metal. Auger decay width (in eV)

Intensity ratio

0.4 (present work) 0.24 [7]

1.04 ± 0.23 0.44 ± 0.16

inelastic L3 photoelectrons emitted by the L3 V PES satellite, both of which lie in the background beneath the singles L2 PES main line (Table 4). The elastic Auger electrons collected in coincidence with the L3 photoelectrons in the background beneath the singles L2 PES main line increases the coincidence CK preceded AES mainline intensity. The ratio of the coincidence CK preceded AES spectral peak intensity to the coincidence L2 –VV one is then given by the following.



IR =



L2 CK + L3 L3

LS + ˜ LM 3



3

LM

(6)

2

Here LM is the L2 PES main-line intensity, LS the L3 photoelec2 3 tron background intensity beneath the L2 PES main line emitted by the L3 V satellite, ˜ LM the inelastic L3 photoelectron background 3 intensity beneath the L2 PES main line emitted by the L3 PES main line,  CK the CK decay width,  x the (x = L2 or L3 )-hole lifetime width. We obtain by Eq. (6) 1.04 ± 0.23 for the intensity ratio of the L3 photoelectron background beneath the L2 PES main line to the intrinsic singles L2 PES main line (Table 5). The L3 photoelectron background intensity is as large as the intrinsic singles L2 PES main line one. When the Auger decay width is 0.24 eV [7], the intensity ratio is 0.44 ± 0.16 (Table 5). The relative L3 photoelectron background intensity is still large. The coincidence CK preceded AES spectral intensity increases by a factor of about 2.7 (or 1.6) because of the elastic Auger electrons collected in coincidence with the L3 photoelectron background beneath the singles L2 PES main line. A small peak KE shift of the coincidence CK preceded AES spectrum to higher KE compared to the singles L3 –VV one is due to the overlap of the former spectrum with the inelastic Auger electron part of the coincidence L2 –VV AES spectrum or/and a poor statistics of APECS apparatus in Ref. [6] (see later). A subtraction of the photoelectron (or Auger electron) background appropriate respectively for the coincidence M4,5 PES (or M4,5 –VV (V = N4,5 ) AES) spectrum and the singles one for Pd or Ag metal to extract out the intrinsic coincidence (or singles) spectra was demonstrated in Refs. [16–18]. Compared to Ref. [18] such a subtraction was not made in Ref. [19]. Thus, in Ref. [19] the M4 –M5 V CK decay width of Pd metal is very much overestimated and the coincidence M4 –M5 V–M5 –VV CK preceded AES main line peak KE is shifted from the singles M5 –VV AES one. The unexpected coincidence AES spectral behavior in Ref. [19] is similar to the one under current investigation. A further analysis of the coincidence L2,3 –VV AES spectrum of Fe is not possible because both the singles L2,3 PES spectrum and the coincidence one for Fe are not reported in Ref. [6]. 4. Coincidence AES spectrum of Co The singles L2,3 –VV AES spectrum of Co measured just above the L3 -level ionization edge and the one far above the L1 -level

ionization edge resemble much the correspondent spectrum of Fe, except for the spin–orbit splitting energy. The intensity ratio (6.7 [1] or 9.9 [7]) of the singles L3 –VV AES spectrum of Co to the singles L2 –VV one is the same as that of Fe [1,7]. The CK decay width of Co is 0.84 eV [7]. We then obtain by Eq. (5) 0.54 eV (or 0.32 eV [7]) for the Auger decay width. The coincidence L2,3 –VV AES spectrum of Co should then be similar to that of Fe. However, the intensity ratio of the coincidence CK preceded AES spectrum to the coincidence L2 –VV one in Ref. [6] is 13.1 ± 2. The ratio is much larger than that (1.56 (or 2.6 [7])) of the CK decay width to the L3 -hole lifetime width. Eq. (2) shows that the coincidence CK preceded AES spectrum of Co should coincide in line shape and peak KE with the coincidence L3 –VV one. However, the former spectrum narrows by as much as 37% compared to the latter one, and the former spectral peak is shifted by 1.1 ± 0.2 eV to lower KE compared to the latter one [6]. The coincidence CK preceded AES spectral intensity of Co is much suppressed in the lower KE tail compared to the singles L3 –VV one. The unexpected anomalous spectral behavior of the coincidence AES spectra of Co compared to Fe raises serious doubt about the coincidence AES spectra of Co reported in Ref. [6]. Recently the L3 PES main line of Cu metal was remeasured by new APECS apparatus in coincidence with the singles L3 –VV (1 G) AES main line. The coincidence L3 PES main line coincides with the singles one in both peak KE and line shape, except for a discrepancy on the lower KE side [20]. The former line is symmetrically narrowed compared to the latter one because the former line is essentially the latter one modulated by the spectral function of a fixed energy analyzer which accepts Auger electrons of a selected KE. As the analyzer is set on the 1 G AES peak KE, the coincidence PES main line shows a symmetric line narrowing compared to the singles one [21]. The coincidence L3 PES main line is well reproduced by the author’s recent many-body calculation, except for a small discrepancy on the lower KE side which is presumably due to the inelastic L3 photoelectron background [21]. However, the coincidence L3 PES spectrum of Cu metal measured by the same group [22] using a different apparatus which is presumably the same as the one in Ref. [6], shows a peak KE shift and an asymmetric line narrowing compared to the singles one. The discrepancy is due to a poor statistics of the apparatus. The singles and coincidence L2,3 –VV AES spectrum (and L2,3 PES one) of Co should be remeasured for a further analysis of the spectrum. 5. AACS and screening time The Auger cascade decay such as the L2 –L3 V CK preceded Auger decay consisting of photoemission, primary Auger electron (CK–electron) emission and secondary Auger electron emission, discussed in the present paper forms a Markovian chain in which the evolution of a probability distribution function is not determined only by the information at that instant but is also governed by the whole history. The secondary Auger electron should not be confused with the “secondary electron” emitted by inelastic scattering of a photoelectron or an Auger electron. We collect in time coincidence by APECS a pair of a photoelectron and a primary Auger electron generated respectively by creation and annihilation of the same intermediate core–hole state, while we collect in time coincidence by AACS a primary Auger electron and a secondary Auger electron generated respectively by creation and annihilation of the same doubly ionized state (Fig. 6). Thus, only features characteristic of the respective event contribute to the APECS or AACS spectrum [23–26]. By explicitly exploiting this unique capability, APECS enables a Markovian chain formed by the photoemission and the primary Auger electron emission of the same intermediate core–hole state, to be examined with unprecedented discrimination, while AACS enables a Markovian chain formed by the primary

M. Ohno / Journal of Electron Spectroscopy and Related Phenomena 171 (2009) 1–17

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Fig. 6. A schematic picture of a set of singles PES, APECS and AACS necessary to obtain the maximum amount of the information of the C–C V–VVV Auger cascade decay. For the sake of simplicity we do not consider the C–C V–C –VV Auger cascade decay, although the same set of singles and coincidence measurements is necessary. See Appendix in Refs. [25] for other sets of singles and coincidence measurements necessary to obtain the maximum amount of the information of the Auger cascade decay.

Auger electron emission and the secondary Auger electron emission of the same doubly ionized state, to be examined with unprecedented discrimination. Thus, a set of APECS and AACS provides so called conditional entropy or conditional information which forms the maximum amount of information of cascade decay together with the information the singles PES or the singles AES provides (Fig. 6) [23–26]. In the present paper so far we discussed the primary AES spectrum and the secondary one measured by APECS in coincidence with photoemission of the selected intermediate core–hole state so that we can examine whether the delocalization time of a valencehole in the doubly ionized state created by the primary Auger decay of the selected intermediate core–hole state is much shorter than the core–hole lifetime of the same doubly ionized state by comparing the coincidence secondary AES spectrum with the intrinsic singles (or coincidence) primary one of the fully relaxed core–hole state. However, when the secondary Auger electrons are collected by APECS in coincidence with the photoelectrons of the selected intermediate core–hole state regardless of the primary Auger electrons generated by annihilation of the same intermediate core–hole state, the coincidence secondary AES spectrum can provide only the conditional information of the correlations between the photoelectron and the secondary Auger electron (Fig. 7). Thus, not only the conditional information of the correlation between the

photoelectron and the primary Auger electron which the primary AES (or PES) spectrum measured by APECS in coincidence with the selected photoelectron (or the selected primary Auger electron) provides, but also that between the primary Auger electron and the secondary Auger electron which the secondary (or primary) AES spectrum measured by AACS in coincidence with the selected primary (secondary) Auger electron provides, are missing (Fig. 7) [23–26]. Measuring the secondary Auger electron by APECS in coincidence with the selected photoelectron does not then provide the maximum amount of information of the cascade decay even together with the primary AES measured in coincidence with the selected photoelectron, and the singles PES because they do not constitute a set of the coincidence and singles measurements necessary for the maximum amount of information of the whole history of the Auger cascade decay [23–26]. As a pair of a photoelectron and a primary Auger electron generated respectively by creation and annihilation of the same intermediate core–hole state are collected by APECS, a primary Auger electron and a secondary Auger electron generated respectively by creation and annihilation of the same doubly ionized state are collected by AACS. If we interprete the doubly ionized state as a primary ionized state, and the primary Auger electron and the secondary one as a photoelectron and a primary Auger electron, respectively, we can see an analogy between APECS and AACS. Such

Fig. 7. APECS by which a secondary Auger electron (A2) is collected in coincidence with a photoelectron (P) generated by a selected intermediate core–hole state (C), and singles PES by which photoelectrons are collected regardless of primary and secondary Auger electrons, do not constitute a set of singles and coincidence measurements necessary to obtain the maximum amount of the information of the Auger cascade decay. The information of not only the correlation between the photoelectron (P) and the primary Auger electron (A1) generated respectively by creation and annihilation of the selected intermediate core–hole state (C) but also that between the primary Auger electron (A1) and the secondary Auger electron (A2) generated respectively by creation and annihilation of the same doubly ionized state cannot be provided by APECS. APECS provides only the information of the correlation between the photoelectron (P) generated by creation of the selected intermediate core–hole state (C) and the secondary Auger electron (A2) generated by annihilation of the doubly ionized state. The doubly ionized state could thus be any doubly ionized state created by annihilation of the selected intermediate core–hole state (C).

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M. Ohno / Journal of Electron Spectroscopy and Related Phenomena 171 (2009) 1–17

an analogy may lead to an incorrect conclusion that as singles PES and APECS constitute a set of singles and coincidence measurements necessary for the maximum amount of information of the primary Auger decay, singles primary AES and AACS which are analogous to singles PES and APECS, respectively, constitute a set of singles and coincidence measurements necessary for the maximum amount of information of the secondary Auger decay. However, without singles PES and APECS the information of the secondary Auger decay which a set of singles primary AES and AACS provides is not satisfactory because a part of the information of the whole history of the Auger cascade decay is missing (see later). It is difficult to collect in coincidence by AACS the primary CK electron emitted by the L2 –L3 V CK decay and the secondary Auger electron emitted by the L3 V–VVV (or L3 V–L3 –VV) Auger decay because the CK–electron KE is very low. Thus, there is no direct experimental evidence to show the correlation between the CK decay and the secondary Auger decay. The coincidence secondary L2 –L3 V CK preceded AES spectrum should be considered as a fortunate case because the spectrum energetically well separated from the ones by secondary Auger decays preceded by other primary Auger decays such as the L2 –MV and L2 –MM Auger decays (M = M2,3 ), coincides in line shape and peak KE with the intrinsic singles L3 –VV one. In general we cannot identify the secondary AES spectrum measured in coincidence with a selected intermediate core–hole state (Fig. 7). For an example we consider the secondary MV–VVV super CK (sCK) spectrum and the secondary MM–VVVV one measured in coincidence with the L3 PES peak (Fig. 8). The secondary MV–VVV sCK spectrum measured in coincidence with the singles L3 PES peak cannot be distinguished from the secondary MM–VVVV one measured in coincidence with the singles L3 PES peak. We have to collect in time coincidence by AACS the primary Auger electron emitted by the L3 –MV (or L3 –MM) Auger decay and the secondary one by the MV–VVV (or MM–VVVV) sCK decay so

that we can tell the secondary MV–VVV sCK spectrum from the secondary MM–VVVV one (Fig. 9). The secondary sCK spectra of MnO overlapping energetically are studied by AACS in Refs. [27,28]. The original prospect of AACS of separating the singles secondary AES spectrum according to the decay channels of a selected doubly ionized state is analogous to that of APECS of separating the singles primary AES spectrum according to the decay channels of a selected intermediate core–hole state [23–26]. A much more unique capability of AACS which has not been explored yet is the one by which we can determine the screening time of a valence-hole created by primary C–C V Auger decay by selecting different primary Auger decay channels so that we can use the C -hole lifetime as an internal clock. Here C and C are core holes. To be able to determine the screening time such as the charge transfer (CT) screening time in a CT system is very important. We collect by AACS a pair of Auger electrons generated respectively by creation and annihilation of the same C V state. If only the secondary C V–VVV Auger decay is observed instead of the secondary C V–C –VV one by AACS in coincidence with the primary C–C V decay, the screening time of the valence-hole is much longer than the C -hole lifetime. Otherwise, the former time is much shorter than the latter one. We can apply Eq. (2) to the C V–VVV and C V–C –VV AACS spectrum measured in coincidence with the primary C–C V decay by replacing R in Eq. (2) by the spectral function of a fixed energy analyzer which accepts primary Auger electrons of a selected KE. The CK electron in Eq. (2) should be replaced by the primary Auger electron by the C–C V decay. The C V–VVV AACS spectrum is narrowed by R compared to the singles C V–VVV AES spectrum. The C V–C –VV AACS spectrum is independent of R because the primary C–C V Auger decay width will not be affected by R. Thus, the C V–C –VV AACS spectrum coincides in line shape and peak KE with the intrinsic singles C –VV AES spectrum.

Fig. 8. A doubly ionized state annihilation of which generates a secondary Auger electron collected by APECS in coincidence with a photoelectron of the selected intermediate core–hole state could be any doubly ionized state created by annihilation of the selected intermediate core–hole state (Fig. 7). As such an example we consider the case in which a selected intermediate core–hole state (C) decays either by C–MV primary Auger decay or by C–MM one. The APECS spectrum provides only the information of the correlation between the photoelectron (P) generated by creation of the selected intermediate core–hole state (C) and the secondary Auger electron (A2) generated by annihilation of the doubly ionized state. The doubly ionized state could be either MV state or MM one generated by annihilation of the intermediate core–hole state (C) so that we cannot tell whether the secondary Auger electron (A2) collected by APECS is generated by annihilation of MV state or by that of MM state.

M. Ohno / Journal of Electron Spectroscopy and Related Phenomena 171 (2009) 1–17

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Fig. 9. As an example of a set of singles PES, APECS, and AACS which can provide the maximum amount of the information of the Auger cascade decay (see Fig. 6) we consider the case in Fig. 8 in which a selected intermediate core–hole state (C) decays either by C–MV primary Auger decay or by C–MM one. The singles PES provides the information of the selected intermediate core–hole state. APECS provides the information of the correlation between the photoelectron (P) and the primary Auger electron (A1) generated respectively by creation and annihilation of the selected intermediate core–hole state (C). AACS provides the information of the correlation between the primary Auger electron (A1) and the secondary Auger electron (A2) generated respectively by creation and annihilation of the same doubly ionized state. Thus, by a set of singles PES, APECS, and AACS we can tell whether the secondary Auger electron (A2) collected by AACS is generated by annihilation of MV state or by that of MM state.

When the screening (delocalization) time of the valence-hole is comparable to any selected C -hole lifetime in the C V state so that both the C V–VVV Auger decay and the C V–C –VV one appear in the AACS spectrum, we have to separate the AACS spectrum into the C V–VVV AACS one and the C V–C –VV AACS one. In this case we measure the C –VV AES spectrum in coincidence with the C -hole PES peak so that we can determine the line profile of the C V–C –VV AACS spectrum, i.e., the intrinsic singles C –VV AES spectrum, by taking into account the line narrowing of the coincidence C –VV AES spectrum by the spectral function of a fixed energy photoelectron analyzer. We can then separate the AACS spectrum into the C V–VVV AACS spectrum and the C V–C –VV one. When the line narrowing of the C V–VVV AACS spectrum by the spectral function of a fixed energy primary Auger-electron analyzer is small, the C V–VVV AACS spectral intensity is the product of the C-level photoionization cross section, the branching ratio of the primary C–C V Auger decay width to the C-hole lifetime width, and the branching ratio of the secondary C V–VVV Auger decay width to the C V-hole lifetime width. The C V–C –VV AACS spectral intensity which is essentially independent of R, is the product of the C-level photoionization cross section, the branching ratio of the primary C–C V Auger decay width to the C-hole lifetime width, the branching ratio of the delocalization width to the C V-hole lifetime width, and the branching ratio of the secondary C –VV Auger decay width to the C -hole lifetime width. Thus, the intensity ratio of the C V–C –VV AACS spectrum to the C V–VVV one is the product of the ratio of the delocalization width to the C -hole lifetime width and that of the secondary C –VV Auger decay width to the secondary C V–VVV one. Once we know the ratio of the secondary C –VV Auger decay width to the secondary C V–VVV one, we can determine the delocalization width. Recently it is shown that the L3 –VV Auger decay width is approximately equal to L3 V–VVV one in Cu metal [12,13]. However, in general the C V–VVV Auger decay width is not necessarily equal to the C –VV one.

The transition from the radiationless resonant Raman scattering to the normal Auger decay in resonant Auger electron spectroscopy (RAES) spectra of a CT systems is discussed in Refs. [29–32] by treating the relaxation and the core–hole decay of the excited core–hole state on the same footing by a many-body theory. When the resonantly excited electron remains at the excited atomic site during the core–hole decay, the RAES spectrum shows the characteristic feature of the resonant Auger–Raman effect, whereas when the excited electron has been transferred from the atomic site before the core–hole decays, the RAES spectrum shows the normal Auger decay. We can determine the delocalization time by measuring the intensity ratio of the normal Auger decay to the spectator (and participant) Auger decay in the RAES spectrum. The core–hole lifetime acts as an internal clock to determine the delocalization time of an excited electron (particle) in a resonantly excited core–hole (one-particle one-hole) state (or that of a valence hole in a doubly ionized (two-hole) state). We can determine the CT time for an excited electron (or a valence hole) created respectively in an unoccupied (or occupied) part of adsorbate–substrate hybridized states. The intensity ratio of the spectator decay in the presence of the spectator electron (or hole) (and the participant decay by the participation of the excited electron) to the normal Auger one in the absence of the spectator electron (or hole) in the resonant AES (RAES) (or AES (AACS)) spectrum provides the ratio of the CT (delocalization) time to the core–hole lifetime. In resonant core–electron excitation an excited core–hole state (or a pair of a core hole and a photoelectron) is selected by fixing the photon excitation energy, while in AACS measurement a doubly ionized state (or a pair of a core hole and a valence hole) is selected by fixing the primary Auger-electron KE. In general when the RAES peak KE is fixed, the RAES peak intensity measured as a function of photon energy is the density of unoccupied states probed by resonant excitation not limited by the intermediate state lifetime. This should be the case also with resonant inelastic X-ray scattering spectroscopy

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(RIXSS) spectra. This is quite analogous to that the PES peak measured in coincidence with a selected singles AES peak KE is not limited by the intermediate core–hole state lifetime. Thus, there is a quite analogy between the two seemingly different spectroscopic studies. 6. AACS spectra of MnO and screening time Recently the Mn MV–VVV (M = M2,3 ) and MM–VVVV super CK (sCK) electron spectra of MnO were measured by AACS in coincidence with the singles L3 –MV AES peak and the L3 –MM one, respectively [27,28]. As shown in the present work in Fe metal the singles L2 –L3 V–L3 –VV CK preceded AES main line coincides in line shape and peak KE with the intrinsic singles L3 –VV AES main line. In Fe the singles L2 –L3 V–L3 –MV (or L2 –L3 V–L3 –MM) CK preceded AES main line should then coincide in both line shape and peak KE with the intrinsic singles L3 –MV (or L3 –MM) AES main line. The L2 –L3 V–L3 –MV–VVV (or L2 –L3 V–L3 –MM–VVVV) CK preceded Auger cascade decay also contributes to the thirdly MV–VVV (or MM–VVVV) AES (sCK) spectrum measured in coincidence with the secondary Auger electron emitted by the CK preceded L3 –MV (or L3 –MM) Auger decay. In Fe the L2 –L3 V–L3 –MV–VVV (or L2 –L3 V–L3 –MM–VVVV) CK preceded AACS spectrum should coincide in line shape and peak KE with the L3 –MV–VVV (or L3 –MM–VVVV) AACS one. If the valence-hole screening time is shorter than or comparable to the M-hole lifetime, there is a possibility that the L2 –L3 V–L3 –MV–M–VV CK preceded Auger cascade decay also contributes to the AACS spectrum. The thirdly (L2 –L3 V–L3 –MV–)M–VV AES (sCK) spectrum measured in coincidence with the secondary Auger electron emitted by the CK preceded L3 –MV Auger decay then coincides in line shape and peak KE with the singles M–VV AES spectrum. The singles primary Mn L2,3 –VV, L2,3 –MV, and L2,3 –MM AES spectra of MnO are reported, however, the correspondent primary (or secondary) AES spectra measured in coincidence with the singles L3 (or L2 ) PES peak are not available [27,28]. Thus, there is no direct experimental evidence to show whether the aforementioned coincidence AES (or AACS) spectral features of Fe metal are also true for MnO. As discussed in Section 5 a set of AACS and singles primary AES is not satisfactory for the maximum amount of information of the Auger cascade decay. We thus have to compensate the lack of the information of the Auger cascade decay by the following analysis. The intensity ratio of the singles L2 –L3 V CK preceded AES line to the singles L3 –VV AES line in MnO is expected to be as large as the one in Mn (0.36 [7]). For core-level photoemission from a transition-metal (TM) compound in a 3dn ground-state configuration, the main line is assigned to a c3dn+1 L configuration (where c and L refer to core and ligand holes), which result from the CT screening by which charge is transferred from a ligand p to an unoccupied TM 3d level to locally screen the photoinduced hole, whereas the satellite corresponds to a poor screened c3dn final state. MnO is a CT insulater but the amount of ligand charge for MnO in the ground state is expected to be small [33]. The Mn core PES spectra of MnO show that the spin–orbit–split Mn 2p level has a small satellite associated with each line, located at binding energy about 6–7 eV higher than the main lines, but the satellite is scarcely visible in the multiplet split 3s and 3p level spectra [33,34]. The 3s and 3p multiplet splittings are primarily via intra-atomic final-state L–S term splittings [34]. To analyze the energetics of the AACS spectra of MnO we employ the CT final-state screening approach. The singles L2 –L3 V–VVV AES satellite is shifted by Ucd –Udd –Udd (d) from the singles L3 –VV AES main line. Ucd (c = L3 ) is similar to Ucd (c = M2,3 ) (Ucd (c = M2,3 ) = 4.1 eV [27]). The KE shift of the singles L2 –L3 V–VVV AES satellite from the singles L3 –VV AES main line is then approximately as large as that of the MV–VVV AACS line from the coincidence M–VV AES

line. The L2 –L3 V–VVV AES satellite is then shifted by about 2 eV toward the higher KE from the L3 –VV AES main line. However, the L3 –VV AES spectrum of MnO does not appear to show the presence of L2 –L3 V–VVV AES satellite of an appreciable intensity (Fig. 2 in Ref. [27]). The valence-hole temporarily localized in the L3 V state in MnO is then screened out prior to the L3 -hole decay so that the L2 –L3 V–L3 –VV decay dominates also in MnO rather than the L2 –L3 V–VVV one. The singles L2 –L3 V–L3 –VV AES main line is shifted by UcL –2UdL from the singles L3 –VV one. Here UdL (or UcL ) is the Coulomb repulsion energy (U) between the valence-hole (or L3 hole) and the ligand oxygen 2p hole. The singles L2 –L3 V–L3 –MV AES main line is shifted by −UdL − UmL + UcL from the singles L3 –MV one. The L3 –MV–VVV AACS line and the L2 –L3 V–L3 –MV–VVV one are shifted respectively by Umd − Udd − Udd (d) and Umd − Udd − Udd (d) − 2UdL + UmL from the singles (or coincidence) M–VV AES line. Here UmL is U between the M2,3 hole and the ligand hole. The singles L2 –L3 V–L3 –MM AES main line is shifted by −2UmL + UcL from the singles L3 –MM one. The L3 –MM–VVVV AACS line is shifted by –Udd (d) + [{Umm − Udd (d2 ) − Udd }/2] from the M–VV AES one, while the L2 –L3 V–L3 –MM–VVVV AACS line is shifted by UmL − 2UdL from the L3 –MM–VVVV one. Here Umm (=10.2 eV for MnO [27]) is U between the two M2,3 holes. The MV–VVV and MM–VVVV AACS spectra do not appear to show any satellite (Fig. 4 in Ref. [27]). The L3 –MV–VVV AACS line then coincides in peak KE with the L2 –L3 V–L3 –MV–VVV one. We obtain UmL = 2UdL . The L2 –L3 V–L3 –MM–VVVV AACS line then coincides in peak KE with the L3 –MM–VVVV one. The valence-holes in the sCK final states are delocalized [27,28] and the ligand holes are also delocalized, UdL = 0. Then UmL = 0 and UcL = 0. The singles L2 –L3 V–L3 –MV (or MM or VV) AES line then coincides in peak KE with the singles L3 –MV (or MM or VV) one. This is in consistent with that the MV (or MM)–VVV (or VVVV) AACS spectrum measured in coincidence with the L2 –L3 V–L3 –MV (or MM) AES peak coincides in peak KE with the AACS one measured in coincidence with the L3 –MV (or MM) AES peak. If the singles L2 –L3 V–L3 –MV (or MM or VV) AES line does not coincide in peak KE with the singles L3 –MV (or MM or VV) one, the MV (or MM)–VVV (or VVVV) AACS spectrum measured in coincidence with the former AES peak does not coincide in peak KE with the AACS one measured in coincidence with the latter AES peak. The L2 –L3 V–L3 –MV–VVV (or MM–VVVV) CK decay preceded AACS spectrum is expected to be broader than the L3 –MV–VVV (or MM–VVVV) AACS one because of the presence of an extra ligand hole created by the screening of the valence-hole in the L3 V state. So long as the L2,3 –VV, L2,3 –MV, and L2,3 –MM APECS spectra of MnO measured in coincidence with the L2,3 PES peak are not available, the present analysis is necessary to warrant that the MV–VVV (or MM–VVVV) AACS spectrum measured in coincidence with the singles L3 –MV (or L3 –MM) AES peak does not contain any satellite such as MVV–VVVV (or MMV–VVVVV) so that the sCK final states are three (or four) valence-hole states. The intensity ratio of the MM–VVVV AACS peak to the MV–VVV one is about 2 [27]. The ratio is equal to that of the sum of the branching ratios of the partial L3 –MM decay width and the L2 –L3 V–L3 –MM one to the sum of the branching ratios of the partial L3 –MV one and the L2 –L3 V–L3 –MV one because the MV hole (or MM holes) decay solely by the MV–VVV (or MM–VVVV) sCK decay. The ratio for Mn atom calculated by an ab initio atomic independent–particle approximation is 1.93 [11]. If the valence-hole in the MV state becomes screened out prior to the M-hole decay, only the L3 –MV–M–VV and L2 –L3 V–L3 –MV–M–VV cascade decay will be observed by AACS in coincidence with the L3 –MV AES peak. However, only the MV–VVV cascade decay is observed in the AACS spectrum of MnO. Thus, the screening time of the valence-hole in the doubly ionized state in

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MnO is longer than the M2,3 -hole lifetime but shorter than the L3 hole lifetime. The experimental L3 -hole lifetime width (FWHM) of Mn is 0.2 eV [7], while the theoretical one of Mn atom is 0.36 eV [14]. The experimental M2,3 -hole lifetime width of Mn is 1.3 eV [8], while the theoretical M2 -hole lifetime width and the M3 one of Mn atom are 1.08 and 1.04 eV, respectively [14]. When charge is transferred from a ligand p to an unoccupied TM 3d level to locally screen the L2 hole in a CT system, the well screened L2 -hole state decays to the poor screened L3 -hole one by the (participant) L2 –L3 V CK decay in which the screening 3d electron participates. If the time scale of the CT screening of the poor screened L3 -hole state, by which charge is transferred from the ligand p to the 3d screening hole created by the CK decay, is shorter than the lifetime of the poor screened L3 -hole state, the poor screened L3 -hole state relaxes to the well screened one. The 3d screening hole in the L3 V state could be temporarily localized in the presence of the L3 hole. This is the case with the L2 –L3 V CK decay in MnO. When the L3 -hole state decays to the M2,3 V state, the M2,3 V state is a poor screened M2,3 -hole state but it differs from the photoemission induced M2,3 -hole state because of the presence of the 3d screening hole in the former state. As the lifetime of the poor screened M2,3 hole in MnO is shorter than the delocalization time of the 3d screening hole which could be temporarily localized in the presence of the M2,3 hole, the M2,3 hole decays before the M2,3 V state relaxes to the M2,3 one. We note that in MnO the screening time of the valence-hole is longer than the L1 -hole lifetime so that the cascade decay of the L1 V satellite may contribute to the singles L2,3 –VV, L2,3 –MV and L2,3 –MM AES spectra of MnO. However, the contribution is very small because as already discussed for Fe the L1 -hole induced decay is small in the singles L2,3 –VV AES spectrum. The authors of Ref. [27] calculated the MV–VVV AACS spectrum by neglecting the effect of 3Uvv (n = 3) = 2Udd + Udd (d) on the unperturbed density of the sCK final VVV states. They calculated the unperturbed density of VVV states as the convolution of three VB (valence band) PES spectra (from which the unhybridized oxygen 2p contribution is presumably subtracted) shifted by 3Udd (not 3Uvv (n = 3)). Here Uvv (n = 3) is the Coulomb hole–hole repulsion energy between a pair of holes in the three-hole state (see Appendix A). Uvv (n) depends on the number (n) of holes in an ionized state. The 3p (or 3s) PES spectral lines rise primarily via the intra-atomic, unscreened final-state L–S term splittings (the 3p(or 3s)–3d exchange interaction) [34]. The CT core–hole screening is then negligible for 3p– (or 3s) level photoemission. However, the multiple valence–hole states created by the M–VV (or MV-VVV or MM-VVVV) sCK decay are CT screened so that the unperturbed DOS of the multiple valence–hole states can be approximated by the convolution of the valence PES spectrum (without the unhybridized oxygen 2p contribution). As a result the CT hole left in the ligand oxygen 2p band contributes to the broadening of the DOS. The calculated MV–VVV AACS spectrum appears to agree better with the experimental MM–VVVV one than with the experimental MV–VVV one. This is because the valence-hole in the MV state is assumed to be delocalized in the calculation so that the calculated MV–VVV AACS spectrum is the unperturbed DOS of VVVV. As the four valence-holes in the sCK final VVVV states are delocalized, the effect of 6Uvv (n = 4) (not 6Udd ) on the convoluted DOS of VVVV is minor. Otherwise, we have to renormalize the convoluted DOS of VVVV by 6Uvv (n = 4) as we renormalize the convoluted DOS of the two valence holes by Udd , by the low–density approximation. In other words we replace Udd by 6Uvv (n = 4) and the convoluted DOS of VV by that of VVVV. In Appendix A we discuss how we determine by AACS the variation of Udd (dn ) with the number (n) of valence-hole already created in an ionized state. Let us assume that the individual M holes in the MM states are equivalent so that their lifetimes are the same. The two M

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holes in the selected MM state then decay simultaneously because the individual M hole decays solely by the M–VV sCK decay and the radiative decay is negligible. Thus, the MM–VVVV AACS spectrum measured in coincidence with the singles L3 –MM (or L2 –L3 V–L3 –MM) AES peak is governed by the MM (selected)–VVVV sCK decay. However, the authors of Refs. [27,28] interpreted the two M holes decay as the MM–MVV–VVVV sCK cascade decay rather than the MM–VVVV sCK decay. Thus, the MM–VVVV AACS spectrum is the sum of the MM–MVV one and the MVV–VVVV one. In the following we show that this is not the case. If the MM–VVVV AACS spectrum consists of the MM–MVV one and the MVV–VVVV one, the MM–MVV AACS peak and the MVV–VVVV AACS one are shifted respectively by Umm − 2Umd + Udd − Udd (m) and 2Umd + Udd (m) − 2Udd − 2Udd (d) − Udd (d2 ) from the M–VV AES one. Here Udd (m) is the Coulomb hole–hole repulsion energy between the two M4,5 holes created in the M2,3 -hole state. The former KE shift is [2.65 − Udd (m)] eV, while the latter one is [1.55 + Udd (m)] eV. It is difficult to evaluate the density of MVV states and Udd (m). The individual M4,5 hole in the MVV state becomes localized in the presence of the M2,3 hole because Umd = 4.1 eV. Consequently Udd (m) becomes so large that the MVV states are likely to form the multiplet. The MM (selected)–MVV AACS spectrum is then essentially a superposition of the spectral functions of respective MVV multiplet states weighted by the respective branching ratios of the MM (selected)–MVV (multiplet) sCK decay width. As Udd (m) is large, the MM–MVV AACS peak is likely to be shifted toward lower KE compared to the M–VV AES one, whereas the MVV–VVVV AACS peak is shifted toward higher KE compared to the M–VV AES one. The MVV–VVVV AACS spectrum measured in coincidence with the selected singles L3 –MM AES peak does not provide the information of the correlation between the MM (selected)–MVV (multiplet) sCK decay and the subsequent MVV (multiplet)–VVVV one (Fig. 10). Here the MVV multiplet states are all the ones created by the MM (selected)–MVV sCK decay preceded by the L3 –MM (selected) Auger decay. Unless we are able to measure the MVV–VVVV sCK decay in coincidence with the MM (selected)–MVV one, we cannot identify the MVV (multiplet) state in the MM (selected)–MVV–VVVV sCK cacade decay (Fig. 11). The MVV–VVVV AACS spectrum measured in coincidence with the selected singles L3 –MM AES peak is essentially a superposition of the spectral functions of respective MVV multiplet states convoluted by the renormalized DOS of the VVVV (delocalized) states, weighted by the respective branching ratios of MM (selected)–MVV (multiplet) sCK decay width and the respective branching ratios of the MVV (multiplet)–VVVV sCK decay width. The MVV–VVVV AACS spectrum then becomes much broader than the DOS of VVVV. This is also the case when the two M4,5 holes in the MVV state are delocalized (Figs. 10 and 11). The MM–MVV AACS spectrum and the MVV–VVVV one depend on the branching ratio of the MM (selected)–MVV (multiplet) sCK decay width and that of the MVV (multiplet)–VVVV sCK decay width. If the MM–VVVV AACS spectrum consists of the MM–MVV one and the MVV–VVVV one, we have to take into account the branching ratios. The M(M)–(M)VV sCK decay width becomes much larger than the M–VV (delocalized) one because the sCK final-state potential becomes much more attractive by the presence of the two localized M4,5 holes and the spectator M2,3 hole, while the M(VV)–VV(VV) sCK decay width becomes similar to the M–VV one because the presence of the two delocalized spectator M4,5 holes in the sCK final state will not affect the sCK decay width (or the sCK final-state potential). Here we note that the sCK electron KE is low. The branching ratio of the M(M) (selected)–(M)VV (specific multiplet) sCK decay width to the lifetime width of the selected MM state becomes the ratio of the M(M) (selected)–(M)VV (spe-

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Fig. 10. A schematic picture of the MM–VVVV AACS spectrum if the MM–VVVV sCK decay consists of the MM–MVV–VVVV sCK cascade decay. The MM–VVVV AACS spectrum then consists of the MM–MVV one (c) and the MVV–VVVV one (d). The MVV–VVVV AACS spectrum (d) is measured by collecting the third Auger electron (A3) in coincidence with the primary Auger electron (A1) but not with the secondary Auger electron (A2). Thus, the information of the correlation between the secondary Auger electron emission (c) and the third Auger electron emission (d) is lost. The third Auger electron (A3) collected in coincidence with the primary Auger electron (Al) can be the one generated by annihilation of any MVV (multiplet) state created by annihilation of the selected MM state. For the sake of simplicity the localization of the two valence holes in the presence of the M hole is not shown in the figure. A set of singles and coincidence measurements shown in the figure does not provide the maximum amount of the information of the C–MM–VVVV cascade decay.

Fig. 11. A schematic picture of a set of the singles and coincidence measurements which provides the maximum amount of the information of the C–MM–MVV–VVVV cascade decay, if the MM–VVVV decay consists of MM–MVV–VVVV cascade decay. As shown in the present paper the MM–VVVV decay does not consist of MM–MVV–VVVV cascade decay. Although it is not shown in the figure, the same set of singles and coincidence measurements provides the maximum amount of the information of the C–MM –M VV–VVVV cascade decay. The C–MM –M VV–VVVV cascade decay in which the M hole and the M hole are created in different atomic shells, occurs, when the M(M )–(M )VV decay time is much shorter than the M (M)–(M)VV one. Here the M and M holes decay solely by the M–VV and the M –VV decay, respectively.

cific multiplet) sCK decay width to the M(M) (selected)–(M)VV (all multiplet) sCK decay width. This is because the lifetime width of the selected MM state is the M(M) (selected)–(M)VV sCK decay width. Here MVV denotes all the MVV multiplet states created by M(M) (selected)–(M)VV sCK decay. The branching ratio of the M(VV) (multiplet)–VV(VV) sCK decay width to the lifetime width of the MVV (multiplet) state is essentially 1.0. Because the two M4,5 -hole lifetime width is much smaller than the M(VV)–VV(VV) sCK decay width so that the MVV-hole lifetime width is essentially the same as the M(VV)–VV(VV) sCK decay width. When we take into account the aforementioned spectral features of the M(M)–(M)VV AACS spectrum and the MVV–VVVV AACS one, the MM–VVVV AACS spectrum does not show either the presence of the M(M)–(M)VV AACS one or that of the MVV–VVVV AACS one. The decay of two holes is a very difficult problem, unless the two holes are the same and decay solely by a single decay channel. AACS

provides prospects of determining the branching ratio of respective Auger-decay width of a selected doubly (or multiply) ionized state so that we can study the variation of the branching ratios in the presence of a spectator hole(s) by comparing the branching ratio of respective Auger-decay width of a selected doubly (or multiply) ionized state with that of a singly ionized state. 7. Auger cascades and AACS The Auger cascades in an iodine atom (iododeoxyuridine (IUdR)) incorporated as an Auger-electron emitter in DNA resulting in DNA double-strand breaks (DSB), are underlying physics of photon activation therapy (PAT) [35]. The effectiveness of the Auger electrons in producing DSB was determined by Monte Carlo simulations [36–39]. In order to estimate the Auger burst size distribution in terms of the number of Auger electrons ejected per an initial hole, or the average number of Auger electrons emitted per Auger cascade

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for an initial vacancy, we evaluate the Auger decay probabilities of multiple holes. The probabilities were approximated by those of a single hole so that the effect of multiple vacancy configurations and energies on the transition rates was completely ignored [36]. The approximation appears to work reasonably well because of the followings. (i) It is the branching ratios of the cascades which govern the number of electrons ejected per an initial hole. (ii) The effect of multiple vacancy configurations and energies on the Auger transition probabilities is minor, whereas that on the (s)CK transition probabilities can be significant [40–42]. However, as the initial M and N holes (except for M4,5 and N4,5 ones) in IUdR decay dominantly by sCK decay [43], M and N holes created in a multiple hole state also decay dominantly by sCK decay so that the effect on the branching ratios of the sCK decay is minor [40]. The lifetime of a multiple-hole state can be much affected by the effect of multiple vacancy configurations and energies on the transition rates. The author took the effect explicitly into account for the first time in ab initio atomic many-body calculations of the two-hole lifetime widths of Ar, Zn, and Cd [40–42]. We consider two holes j and k created in different atomic shells in an atom. If they are not interacting, their lifetime width Tjk is the sum of Tj and Tk . Tj (or Tk ) is the lifetime of a single j (or k)-hole state. Otherwise, we have to take explicitly into account the time ordering of respective decay events of the two holes so that Tjk is the sum of Tj (k) and Tk (j). Tj (k) is the j-hole decay width when k hole acts as a spectator during the jhole decay, i.e., the j(k) → Fj (k) spectator decay width T(j(k) → Fj (k)) renormalized by the spectral function of three holes Fj (k), summed over the two holes Fj created by the j(k) → Fj (k) decay channels prior to the k-hole decay to Fk (Fj ). We assume that the two holes Fj in Fj (k) decay after the k-hole decays to Fk (Fj ). The lifetime width of the spectral function of Fj (k) is then Tk (Fj ). Tk (Fj ) is the k-hole decay width when the two holes Fj act as spectators during the k-hole decay, i.e., the k(Fj ) → Fk (Fj ) spectator decay width T(k(Fj ) → Fk (Fj )) renormalized by the spectral function of four holes Fk (Fj ), summed over the two holes Fk created by the k(Fj ) → Fk (Fj ) decay after the j-hole decays to Fj . To evaluate T(j(k) → Fj (k)) (or T(k(Fj ) → Fk (Fj )) we have to take explicitly into account the effect of spectator k (or Fj )-hole(s) on the Auger (or CK)-electron wavefunction [40–42]. Thus, “spectator(s)” participates in the decay. Tk (j), i.e., the k-hole decay width when j hole acts as a spectator during the k-hole decay, is given by exchanging the indices j and k in the aforementioned formula for Tj (k). We assume that two holes F˜ k in F˜ k (j) decay after j-hole decays. We note that if k-hole acts as a spectator for all jhole decay channels, i.e., k-hole is in the most outer shell, Tjk is Tj (k). However, Tj (k) is not equal to Tj because of the presence of spectator k hole. We consider i → jk → Fj (k) → Fk (Fj ) and i → jk → F˜ k (j) → F˜ j (F˜ k ) Auger cascades. We assume that the jk → Fj (k) and the jk → F˜ k (j) AACS lines measured in coincidence with the i → jk AES line are well separated. The intensity ratio of the jk → Fj (k) AACS line to the jk → F˜ k (j) one is (Tj (k)/Tk (j)). Using the i-hole lifetime width we determine Tjk from the singles i → jk AES line width. We can then determine Tj (k) and Tk (j). The k(Fj ) → Fk (Fj ) (or j(F˜ k ) → F˜ j (F˜ k )) AACS line measured in coincidence with the jk → Fj (k) (or jk → F˜ k (j)) AES line provides the branching ratio of T(k(Fj ) → Fk (Fj )) (or T(j(F˜ k ) → F˜ j (F˜ k ))) of k(Fj ) (or j(F˜ k )) state. Thus, AACS projects the probabilities of respective cascade events of a multiple-hole state on the Auger-electron KE space. 8. Conclusion It is shown by a many-body theory that (i) when the M4,5 hole created by the CK decay delocalizes rapidly prior to the L3 -hole decay, the singles CK preceded AES spectrum coincides in line shape and peak KE with the intrinsic singles L3 –VV one.

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The L2 -hole lifetime does not broaden the former spectrum. This is also the case with the Auger decay following the L1 –L2,3 V CK decay or the L1 V (or L2,3 V) shakeup/off excitations. In general the singles C–C V–C –C V–C –VV AES spectrum coincides in line shape and peak KE with the intrinsic singles C –VV one. This explains why there is no line shape variation with photon energy in the singles L3 –VV AES main line of Fe (or Co). (ii) The L2 –L3 V–L3 –VV AES main line of Fe (or Co) measured in coincidence with the singles L2 PES peak coincides in line shape and peak KE with the intrinsic singles L3 –VV AES main line. In general the coincidence C–C V–C –C V–C –VV AES main line coincides in line shape and peak KE with the intrinsic singles C –VV AES one. (iii) When the resolution width of the fixed energy analyzer in Ref. [6] is taken into account, the coincidence L3 –VV AES spectrum coincides in line shape with the intrinsic singles one, however, the coincidence L2 –VV AES spectrum becomes narrower than the intrinsic singles one. (i) to (iii) are in accord with the experimental findings in Refs. [1–4,6]. In the light of (i) to (iii) we determined the Auger decay width (0.4 eV) of the L3 -hole state in Fe metal by analyzing the singles and coincidence AES spectra in Ref. [6]. The Auger decay width agrees well with the one calculated by an ab initio atomic independent–particle approximation (0.41 eV [14]). The percentage contributions to the singles L2,3 –VV AES spectrum of Fe is also determined. The present theory shows that the intensity ratio of the coincidence CK preceded AES spectrum to the coincidence L2 –VV one is equal to the ratio of the CK decay width to the L3 -hole lifetime width so that we can determine the CK (or Auger) decay width from the former ratio and the singles L2 PES line width. However, the former ratio (4.3 ± 0.6) of Fe reported in Ref. [6] is much larger than the latter one (1.6 (or 2.67)). This is because of the Auger electrons collected in coincidence with the L3 photoelectron background beneath the singles L2 PES main line. The L3 photoelectron background intensity is found to be as large as the intrinsic singles L2 PES main line one. A subtraction of the background appropriate respectively for the coincidence AES (or PES) spectrum and the singles one is necessary for comparison between the two spectra. In contrast to Fe the present analysis raises serious doubt about the coincidence AES spectra of Co reported in Ref. [6] because the spectra show unexpected anomalous spectral line shape changes from Fe to Co. The 2p hole created in the partially filled d-band metal is effectively screened by the electron occupying the empty orbital. This results in an increase of nearly one electron in the valence band charge [44]. The two-hole state created L2 –L3 V CK decay is the unscreened L3 -hole state. As the metallic screening time of L3 hole is shorter than the L3 -hole lifetime, the unscreened L3 -hole state relaxes to the screened one prior to the L3 -hole decay. In other words the attractive L3 -hole potential becomes effectively screened before L3 -hole decays so that the valence hole created by the CK decay hops away from the ionized atomic site. The 2p hole created in the fully filled d-band metal cannot be effectively screened because the screening electron can occupy the s and p orbitals lying above d band [44]. Thus, the valence hole created by the L2 –L3 V CK decay remains localized during the L3 -hole decay. We discussed the prospect of determining the screening time of a valence hole in a doubly ionized state by collecting by AACS in coincidence a pair of Auger electrons generated respectively by creation and annihilation of the same doubly ionized state. We use the lifetime of a core hole in a doubly ionized state created by primary Auger decay as an internal clock. We analyzed the Mn M2,3 V–VVV and Mn M2,3 M2,3 –VVVV AACS spectra of MnO reported in Refs. [27,28]. The screening time of the valence-hole in the doubly ionized state in MnO is shorter than the L3 -hole lifetime but longer than the M2,3 -hole one. The Mn MM–VVVV (M=M2,3 ) AACS spectrum of MnO measured in coincidence with the singles Mn L3 –MM

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M. Ohno / Journal of Electron Spectroscopy and Related Phenomena 171 (2009) 1–17

AES peak was analyzed. The two M holes decay simultaneously by the MM–VVVV decay rather than by the MM–MVV–VVVV cascade one. We discussed several unexploited prospects for AACS. (i) Using the core–hole lifetime in a doubly ionized state as an internal clock we determine by AACS the CT screening time in a CT system such as transition-metal compounds and adsorbates. (ii) We determine by AACS the variation in the Coulomb repulsion energy with an increase of hole. (iii) We determine by AACS the variation in branching ratios of Auger cascades and core–hole lifetime with an increase of hole. For an example AACS provides prospects for analyzing Auger cascades in IUdR incorporated in DNA. Finally we note that as the primary AES spectrum measured by APECS in coincidence with the singles PES elastic peak is much less affected by the inelastic primary Auger electrons compared to the singles primary AES one, the secondary AES spectrum measured by AACS in coincidence with the singles primary AES elastic peak is much less affected by inelastic secondary Auger electrons compared to the singles secondary AES spectrum. Appendix A We can study by AACS the variation in the Coulomb hole–hole repulsion energy U with the number of valence-hole in an ionized state. The n valence-hole energy Edn , is given by the following [45]. Edn = nEd − −

n(n − 1) n(n − 1)(n − 2) U− 2! 3!

n(n − 2)(n − 1) 4!

2



2

d U dn2



− ···

 dU dn

(A1)

Ed is the single valence-hole energy. U(dn ), i.e., U between two valence holes created in an ionized state in which n valence-holes are already created, is given by the following. n

U(d ) = U + n

 dU dn

n2 + 2!



d2 U dn2



+ ···

(A2)

Using Eqs. (A1) and (A2) we find that the M2,3 V–VVV AACS peak and the M2,3 M2,3 –VVVV one are shifted respectively by Umd − U − U(d) and −U(d) + [{Umm − U(d2 ) − U}/2] from the coincidence M2,3 –VV one. Umm = 10.2 eV, Umd = 4.1 eV, and U = 0.65 eV are empirically determined for MnO from the L3 –M2,3 M2,3 AES peak KE, the L3 –M2,3 V one and the M2,3 –VV one, respectively [27]. Using the peak KE shifts (2.1 eV) of the M2,3 V–VVV AACS line and the M2,3 M2,3 –VVVV one from the coincidence M2,3 –VV AES line, we obtain U(d) = 1.35 eV and U(d2 ) = 2.65 eV. Neglecting in Eqs. (A1) and (A2) the terms higher than the second-order derivative of U with respect to n, we obtain the followings.

 dU

dn d2 U dn2

= 0.6 eV

(A3)

 = 0.4 eV

(A4)

Neglecting further in Eqs. (A1) and (A2) the second-order derivative of U with respect to n, we obtain 0.7 eV for the first-order derivative of U with respect to n. We then obtain 2.4 eV for the KE shift of the M2,3 M2,3 –VVVV AACS peak from the coincidence M2,3 –VV AES line. It agrees well with the experimental KE shift (2.1 eV). Thus, the linear response approximation for the variation in U with n is valid for the four valence-hole state in MnO. The localization and delocalization of the three valence-hole state depends on the ratio of (3Uvv (n = 3)/3W). Here Uvv (n = 3) is the Coulomb hole–hole repulsion energy between a pair of holes in the three valence-hole state renormalized by the change

Fig. 12. A schematic picture showing how we decompose the Coulomb hole–hole repulsion energy Uvv (n) between a pair of hole in a n-hole state in terms of the Coulomb hole–hole repulsion energy U(dn ) between a pair of hole additionally created in an ionized state in which n holes are already present. For a two-hole state Uvv (n = 2) = U. For a three-hole state 3Uvv (n = 3) = 2U + U(d). For a four-hole state 6Uvv (n = 4) = 3U + 2U(d) + U(d2 ). In general Uvv (n) =

n−2 i=0

(n − 1 −

i)U(d )/[n(n − 1)/2]. We obtain U = Uvv (n = 2), U(d) = 3Uvv (n = 3) − 2Uvv (n = 2) and U(d2 ) = 6Uvv (n = 4) − 6Uvv (n = 3) + Uvv (n = 2). In general U(di−2 ) = (i(i − 1)/2)Uvv (n = i) − (i − 1)(i − 2)Uvv (n = i − 1) + ((i − 2)(i − 3)/2)Uvv (n = i − 2). i

in U by the presence of an extra valence-hole. Using Eqs. (A1) and (A2) we obtain 3Uvv (n = 3) = 2U + U(d) (Fig. 12). The ratio is then (0.88/W) so that the three valence-holes are delocalized in MnO. The localization and delocalization of the four valence-hole state depends on the ratio of (6Uvv (n = 4)/4W). Here Uvv (n = 4) is the Coulomb hole–hole repulsion energy between a pair of holes in the four valence-hole state renormalized by the presence of extra two valence holes. Using Eqs. (A1) and (A2) we obtain 6Uvv (n = 4) = 3U + 2U(d) + U(d2 ) (Fig. 12). The ratio is then (1.825/W). The four valence-holes are then delocalized in MnO. With an increase in the number of valence-holes the valence-holes tend to be less delocalized in the present case. Uvv (n = number of holes in an ionized state) is equal to U = Uvv (n = 2) in many literatures. Such an approximation ignores the variation in Uvv (n) with a number of holes so that one draws an incorrect conclusion such as that if two holes are localized, three holes are also localized. The screening of holes depends on the number of holes. AACS provides the prospect for determining the variation in Uvv (n) with the number (n) of holes in an ionized state. References [1] D.D. Sarma, S.R. Barman, R. Cimino, C. Carbone, P. Sen, A. Roy, A. Chainani, W. Gudat, Phys. Rev. B48 (1993) 6822. [2] P. Unsworth, N. Brooks, J.M.C. Thornton, M. Sancrotti, S. D’Addato, L. Duó, P.T. Andrews, P. Weightman, J. Electron. Spectrosc. Relat. Phenom. 72 (1995) 205. [3] S. D’Addato, P. Luches, R. Gotter, L. Floreano, D. Cvetko, A. Morgante, A. Newton, D. Martin, P. Unsworth, P. Weightman, Surf. Rev. Lett. 9 (2002) 709. [4] S. Iacobucci, F. Sirotti, M. Sacchi, G. Stefani, J. Electron. Spectrosc. Relat. Phenom. 123 (2002) 397. [5] M. Ohno, G. Wendin, J. Phys. B12 (1979) 1305. [6] C.P. Lund, S.M. Thurgate, A.B. Wedding, Phys. Rev. B 55 (1997-II) 5455 (in this reference the Auger electron KE scale in the coincidence AES spectra of Co is incorrect. The second column in table II should read the peak intensity ratio of the coincidence CK preceded AES spectrum to the coincidence L2 –VV one. Otherwise, it is unphysical. In table II “%” should read “eV”). [7] R. Nyholm, N. Mårtensson, A. Lebugle, U. Axelsson, J. Phys. F11 (1981) 1727. [8] J.C. Fuggle, S.F. Alvarado, Phys. Rev. A22 (1980) 1615. [9] Yu. Kucherenko, P. Rennert, J. Phys. C9 (1997) 5003. [10] J.H. Scofield, J. Electron. Spectrosc. Relat. Phenom. 8 (1972) 129. [11] M.H. Chen, B. Crasemann, H. Mark, Atomic Data Nucl. Data Tables 24 (1979) 13. [12] M. Ohno, J. Electron. Spectrosc. Relat. Phenom. 164 (2008) 1. [13] M. Ohno, J. Electron. Spectrosc. Relat. Phenom. Erratum 168 (2008) 46.

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