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XPS-valence bands of iron, cobalt, palladium and platinum
Volume 57A, number 3
PHYSICS LEUERS
14 June 1976
XPS-VALENCE BANDS OF IRON, COBALT, PALLADIUM AND PLATINUM H. HOCHST, S. HUFNER and A. GOLDMANN Fachbereich Physik, Unjversjttft des Saarlandes, 6600 Saarbrdcken, Germany Received 20 April 1976 XPS valence band spectra of iron, cobalt, palladium and platinum are reported. They show good agreement with theoretical density of states curves that have been corrected for instrumental resolution, electron-hole interaction, matrix element modulation, lifetime of the photohole and inelastic electron electron scattering.
In a series of papers, Smith et al. [11 have investigated in how far it is possible to probe the bandstructure of d band metals by photoelectric (UPS and XPS) measurements. As for the density of states (DOS), they found [2] that for the noble metals Cu, Ag and Au the XI’S valence band spectra are in good agreement with theoretical DOS curves that have been convoluted with the spectrometer resolution function. For the open d shell metals, however, the agreement was found to be quite less satisfactory. We report in this note, that after properly taking into account several corrections, the experimental XPS valence band spectra for the open d shell metals Fe, Co, Pd and Pt can be reproduced remarkably well from theoretical DOS functions. There are five effects that modify an XPS valence band spectrum if compared with a theoretical DOS: (1) instrumental resolution, (2) matrix elements modulation across the width of the d-band, (3) lifetime of the photohole, (4) interaction of the photohole with the conduction electrons and (5) inelastic electron electron scattering. It is difficult to remove the effects of all these mechanisms from a measured XPS spectrum in order to compare it directly with a theoretical DOS curve. It was therefore chosen to apply all the corrections (l)—(5) to the theoretical DOS curves, thereby creating a “theoretical” XI’S spectrum that can then be compared with the experimental XPS spectrum. The corrections were applied in such a way as to give the best visual agreement between the theoretical and experimental spectrum. Now it will be briefly discussed how the mentioned corrections were applied, (1) The instrumental resolution function was determined from the Fermi edge of Ag-metal and found to be a slightly asymmetric Gaussian curve with r~ = 0.55 eV(FWHM).
(2) The larger photoelectric cross section for the eg electrons as compared to the t2g electrons levels tends to decrease the intensity in the lower portion of the band [3]. In first order this can be accounted for by multiplying the intensity by (I + ?~E) 1, where E is the energy with respect to the center of the band and A is an adjustable parameter. (3) The lifetime of the photohole was assumed to produce a broadening that can be represented by a Lorentzian line shape of width ~h’ where r~ was treated as an energy-dependent, adjustable parameter. For its energy dependence near EF a Fermi distribution function was chosen of width W, with the halfheight point of this distribution positioned at energy W below the experimental Fermi edge EF. (4) The hole-conduction electron interaction was taken into account by using the lmeshape function of Doniach and Sunjic [4], where a is the asymmetry parametet. This formula describes the hole-conduction electron coupling well for core levels [5]. It has to be noted however that for open d band metals, this function is only a rough approximation, because the electron-hole pair density of states is not taken into account properly [6].. (5) The electron electron scattering tail was measured in the vicinity of core lines and then corrected for in the valence band by assuming that the strength of the scattered electron distribution is proportional to the integral over the strength of the unscattered electrons. Fig. 1 shows a comparison of the experimental with the theoretical energy distribution curves for Fe [7], Co [8], Pd [9] and Pt [101 and the table lists the relevant parameters used to perform the fits. The experimental data were obtained from evaporated 265
Volume 57A, number 3
PHYSICS LETTERS
14 June 1976
Table 1 Correction parameters used to calculate the photo electron
86
~
2
spectrum fromFethe theoretical Co density of states. Pd
Pt
1) aS/B ~ x[eV] —13)
r’hleV]4)
0.2 0.4 —0.13
0.18 0.32 —0.13
0.1 0.19 —0.23
0.15 0.19 —0.13
0.78
0.78
0.47
0.47
.4
~x 75 z 0 ~ z 5,0
1) aS/B: is the asymmetry parameter as defined by the lineshape function in ref. [4]. W[eV]5) 0.94core line, taken 0.31 from ref.0.31 2) a~~j~: ~me1.44 ~ ~ but for
I
02.5 w Q
0
-
‘I,
of rh near the Fermi energy.
~—15 z ~10 z
sent day XPS instruments. It seems therefore unlikely that by improving the resolution of these instruments more information on DOS curves of open d shell system can be obtained.
05 lx
00 -J
15
We thank Dr. G.K. Wertheim (Bell Laboratories,
10
Murrayused I~ll) some of the grams infor thisproviding work. This work was computer supportedproby the Deutsche Forschungsgemeinschaft.
5 0
14 12 10 8 6 4 2 EF 2 BINDING ENERGY 1eV]
Fig. 1. Comparison of experimental spectra with corrected theoretical density of states curves.
samples with a Hewlett Packard 595oA spectrometer. The agreement between theory and experiment is as good as might be expected in view of the many approximations made. One can suspect that the problems in the lower part of the d band for Pt are caused by the spin orbit coupling. The main conclusion from this work is that, if proper care is taken of the above mentioned correctiôns, photoelectron distribution curves for XPS experiments can quite successfully be calculated from first principle bandstructure calculations. It is also particularly noteworth that the life-time broadenings are of the order of the experimental resolution in pre266
[5] and this work. 3) Parameter in the intensity modulation function 1(E) ~ (1 +xE)~. 4) 1’h~Lorentzian life time width (FWHM). 5) Width of the Fermi distribution that governs the variation
References [1] N.y. Smith, G.K. Wertheim, S. Htlfner and M.M. Traum, Phys. Rev. BlO (1974) 3197 and references therein.
[21G.K. Wertheim, N.y. Smith, M.M. Traum and D.N.E. Buchanan, Phys. Letters 49A (1975) 191. [3] V.V. Nemoshkalenko, V.G. Aleshin, Yu.N. Kucherenko
[4]
[5] [6] [7] [8]
[9] [10]
and L.M. Sheludchenko, J. Electron Spectrosc. 6 (1975) 145. S. Doniach and M. Sunjic, J. Phys. C3 (1970) 285. 5. Htlfner, G.K. Wertheim and J.H. Wernick, Solid State Communications 17 (1975) 417. G.K. Wertheim and L.R. Walker, Preprint (1976). M. Singh, C.S. Wang and J. Callaway, Phys. Rev. Bli (1975) 287. E.P. Wohlfarth, J. Appl. Phys. 41(1970)1205. F.M. Mueller, A.J. Freeman, J.O. Dimmock and A.M. Furdyna, Phys. Rev. Bi (1970) 4617. F.M. Mueller, J.W. Garland, M.H. Cohen and K.H. Bennemann, Ann. Phys. 67 (1971) 19.
PHYSICS LEUERS
14 June 1976
XPS-VALENCE BANDS OF IRON, COBALT, PALLADIUM AND PLATINUM H. HOCHST, S. HUFNER and A. GOLDMANN Fachbereich Physik, Unjversjttft des Saarlandes, 6600 Saarbrdcken, Germany Received 20 April 1976 XPS valence band spectra of iron, cobalt, palladium and platinum are reported. They show good agreement with theoretical density of states curves that have been corrected for instrumental resolution, electron-hole interaction, matrix element modulation, lifetime of the photohole and inelastic electron electron scattering.
In a series of papers, Smith et al. [11 have investigated in how far it is possible to probe the bandstructure of d band metals by photoelectric (UPS and XPS) measurements. As for the density of states (DOS), they found [2] that for the noble metals Cu, Ag and Au the XI’S valence band spectra are in good agreement with theoretical DOS curves that have been convoluted with the spectrometer resolution function. For the open d shell metals, however, the agreement was found to be quite less satisfactory. We report in this note, that after properly taking into account several corrections, the experimental XPS valence band spectra for the open d shell metals Fe, Co, Pd and Pt can be reproduced remarkably well from theoretical DOS functions. There are five effects that modify an XPS valence band spectrum if compared with a theoretical DOS: (1) instrumental resolution, (2) matrix elements modulation across the width of the d-band, (3) lifetime of the photohole, (4) interaction of the photohole with the conduction electrons and (5) inelastic electron electron scattering. It is difficult to remove the effects of all these mechanisms from a measured XPS spectrum in order to compare it directly with a theoretical DOS curve. It was therefore chosen to apply all the corrections (l)—(5) to the theoretical DOS curves, thereby creating a “theoretical” XI’S spectrum that can then be compared with the experimental XPS spectrum. The corrections were applied in such a way as to give the best visual agreement between the theoretical and experimental spectrum. Now it will be briefly discussed how the mentioned corrections were applied, (1) The instrumental resolution function was determined from the Fermi edge of Ag-metal and found to be a slightly asymmetric Gaussian curve with r~ = 0.55 eV(FWHM).
(2) The larger photoelectric cross section for the eg electrons as compared to the t2g electrons levels tends to decrease the intensity in the lower portion of the band [3]. In first order this can be accounted for by multiplying the intensity by (I + ?~E) 1, where E is the energy with respect to the center of the band and A is an adjustable parameter. (3) The lifetime of the photohole was assumed to produce a broadening that can be represented by a Lorentzian line shape of width ~h’ where r~ was treated as an energy-dependent, adjustable parameter. For its energy dependence near EF a Fermi distribution function was chosen of width W, with the halfheight point of this distribution positioned at energy W below the experimental Fermi edge EF. (4) The hole-conduction electron interaction was taken into account by using the lmeshape function of Doniach and Sunjic [4], where a is the asymmetry parametet. This formula describes the hole-conduction electron coupling well for core levels [5]. It has to be noted however that for open d band metals, this function is only a rough approximation, because the electron-hole pair density of states is not taken into account properly [6].. (5) The electron electron scattering tail was measured in the vicinity of core lines and then corrected for in the valence band by assuming that the strength of the scattered electron distribution is proportional to the integral over the strength of the unscattered electrons. Fig. 1 shows a comparison of the experimental with the theoretical energy distribution curves for Fe [7], Co [8], Pd [9] and Pt [101 and the table lists the relevant parameters used to perform the fits. The experimental data were obtained from evaporated 265
Volume 57A, number 3
PHYSICS LETTERS
14 June 1976
Table 1 Correction parameters used to calculate the photo electron
86
~
2
spectrum fromFethe theoretical Co density of states. Pd
Pt
1) aS/B ~ x[eV] —13)
r’hleV]4)
0.2 0.4 —0.13
0.18 0.32 —0.13
0.1 0.19 —0.23
0.15 0.19 —0.13
0.78
0.78
0.47
0.47
.4
~x 75 z 0 ~ z 5,0
1) aS/B: is the asymmetry parameter as defined by the lineshape function in ref. [4]. W[eV]5) 0.94core line, taken 0.31 from ref.0.31 2) a~~j~: ~me1.44 ~ ~ but for
I
02.5 w Q
0
-
‘I,
of rh near the Fermi energy.
~—15 z ~10 z
sent day XPS instruments. It seems therefore unlikely that by improving the resolution of these instruments more information on DOS curves of open d shell system can be obtained.
05 lx
00 -J
15
We thank Dr. G.K. Wertheim (Bell Laboratories,
10
Murrayused I~ll) some of the grams infor thisproviding work. This work was computer supportedproby the Deutsche Forschungsgemeinschaft.
5 0
14 12 10 8 6 4 2 EF 2 BINDING ENERGY 1eV]
Fig. 1. Comparison of experimental spectra with corrected theoretical density of states curves.
samples with a Hewlett Packard 595oA spectrometer. The agreement between theory and experiment is as good as might be expected in view of the many approximations made. One can suspect that the problems in the lower part of the d band for Pt are caused by the spin orbit coupling. The main conclusion from this work is that, if proper care is taken of the above mentioned correctiôns, photoelectron distribution curves for XPS experiments can quite successfully be calculated from first principle bandstructure calculations. It is also particularly noteworth that the life-time broadenings are of the order of the experimental resolution in pre266
[5] and this work. 3) Parameter in the intensity modulation function 1(E) ~ (1 +xE)~. 4) 1’h~Lorentzian life time width (FWHM). 5) Width of the Fermi distribution that governs the variation
References [1] N.y. Smith, G.K. Wertheim, S. Htlfner and M.M. Traum, Phys. Rev. BlO (1974) 3197 and references therein.
[21G.K. Wertheim, N.y. Smith, M.M. Traum and D.N.E. Buchanan, Phys. Letters 49A (1975) 191. [3] V.V. Nemoshkalenko, V.G. Aleshin, Yu.N. Kucherenko
[4]
[5] [6] [7] [8]
[9] [10]
and L.M. Sheludchenko, J. Electron Spectrosc. 6 (1975) 145. S. Doniach and M. Sunjic, J. Phys. C3 (1970) 285. 5. Htlfner, G.K. Wertheim and J.H. Wernick, Solid State Communications 17 (1975) 417. G.K. Wertheim and L.R. Walker, Preprint (1976). M. Singh, C.S. Wang and J. Callaway, Phys. Rev. Bli (1975) 287. E.P. Wohlfarth, J. Appl. Phys. 41(1970)1205. F.M. Mueller, A.J. Freeman, J.O. Dimmock and A.M. Furdyna, Phys. Rev. Bi (1970) 4617. F.M. Mueller, J.W. Garland, M.H. Cohen and K.H. Bennemann, Ann. Phys. 67 (1971) 19.