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Electron correlation effects in the valence band photoemission spectra of cooper dichloride
~
Solid State Communications, Printed in Great Britain.
Voi.42, No.3, pp.165-168,
ELECTRON CORRELATION EFFECTS
1982.
0038-1098/82/150165-04503.00/0 Pergamon Press Ltd.
IN THE VALENCE BAND PHOTOEMISSION
SPECTRA OF COPPER DICHLORIDE
Gerrit van der Laan Laboratory
of Inorganic Chemistry and Laboratory of Physical Chemistry, The University of Groningen, Nijenborgh 16, 9747 AG Groningen, The Netherlands. ( Received 8 December
1981 by A.R. Miedema )
He I, He II and AI K~ photoemission measurements of the valence band of CuCI 2 are reported. The presence of the 3dS-like satellite indicates the strong correlation effects in the final state and the breakdown of the one-particle model. It is shown that the reduction of the satellite intensity in the valence band compared with the core hole emission is caused by the delocalization of the photo-hole. The satellite intensity in resonance with the super-Coster-Kronig decay is calculated.
The valence band photoemission spectra of compounds with initially full valence bands can be interpreted with a one-particle density of states (DOS) model. Also for compounds with partly filled valence bands, but with negligible Coulomb interactions between the final state holes, the spectrum reflects the DOS. Several authors have attempted to interpret in the same way the UPS and XPS valence band spectra of compounds, in which large Coulomb interactions are present between the final state holes. Some examples for this are Fe304 [I], Fe, Co and Ni [2] and the 3d transition metal pyrites [3,4]. However, we think that the valence band spectra of these compounds cannot be described adequately within a one-particle model. Penn [5] has outlined this already for the Ni valence band. The presence of a 3d -like satellite is clear evidence for the breakdown of the one-particle model in CuCI 2. In a previous paper [6] we have shown that the core hole emission spectra of Cu dihalides could be explained with a model, which takes into account the strong Coulomb interaction between the final state holes. In this paper this model is extended to the case of valence band emission and the results are compared with UPS and XPS measurements. To our knowledge there are no UPS reports on solid CuCI 2 in the literature. The compound is very hygroscopic and it slowly decomposes into monohalide and halogen gas. The powdered material charges inhomogeneously during the photo-ionization process. This results in a low counting rate and a severe line broadening, especially at low kinetic energies as in UPS. We managed to avoid these charging effects by preparing a thin film. For this purpose purified CuCI 2 was dissolved in a mixture of ethanol and acetone (I:I). In a nitrogen atmosphere a degreased Cu metal substrate was spread with a thin film of this solution, and the solvent was evaporated. Under the exclusion of air the sample was inserted into a VG ADES 400 spectrometer, and the remaining thin film was checked for its composition with XPS. Only very weak carbon and oxygen lines were observed, and the Cu core spectra had the proper satellite
structure of CuCI_. The UPS and XPS spectra are given in Fig.71 and Fig. 2, respectively. The Fermi level of the Cu metal substrate has been taken as the zero binding energy reference. The UPS spectra have not been corrected for background and analyzer transmission. The transmission is inversely proportional to the kinetic energy. This gives raise to the large increase in the intensity for He I at higher binding energies. The small peaks at 2.5 and 3.0 eV may be due to small amounts of CuCI, caused by the decomposition of the dihalide at the
i
/HeZ
.
j 0
rr
'
i
,
4
I
,
8
Binding energy F i g . 1 . He I a n d He I I emission f r o m CuC12.
I
12
(eV)
excited
valence
band
surface. In the AI Ks and He II spectra a 3d 8like final state is observed. In the He I spectrum this structure could not be resolved because of the small Cu 3d cross-section at this energy. Table 1. Atomic cross-section ratios of C1 3p a n d Cu 3d a s g i v e n b y G o l d m a n n e t and S c o f i e l d [8]. Radiation He I He I I A1 KS
165
source
0(C1
the al.
3p6)/O(Cu 3.50 0.30 0.41
[7]
3d 1 ° )
Vol• 42, No. 3
ELECTRON CORRELATION EFFECTS
166
around the Cu with 4 C1 at a distance 2.30 and 2 C1 at 2.95 ~. The local crystal field at the Cu site has approximately D4h sym~netry. The 3d orbitals with b 2 and e symmetry of a particular Cu atom ar§ hybridized with linear combinations of p~-type orbitals of the neighbouring CI atoms with b 2 and e symmetry. The 3d orbitals with a. gand b, g symmetry are hybridized with linearJ§ombina~ons of pO-type orbitals with a! and b] syn~netry. In the g~ound state onegeleetro~ is missing in the b~ . Working with holes, rather than with ei§ctrons, the ground state wave function can be written as
CI 3s
~g = b ~]g = d+cosO - Lisin@ L
8 12 Binding energy (eV) F i g . 2 . A1 K~ e x c i t e d f r o m CuC12 .
valence
16
20
band emission
T a b l e 2 . The e x p e r i m e n t a l energy positions and i n t e n s i t i e s for the peaks observed in v a l e n c e b a n d o f CuC12. T h e t o t a l intensity normalized to one.
main band 3d 8 3d 8 3d s
3F iD,3p IG
Binding He I I 5.0 11.2 13.0 13.7
(I)
where d and L are metal d and ligand p orbitals, respectively, and the parameter cos@ describes the covalent mixing. We assume that metal d and ligand p orbitals are orthogonal. For the evaluation of the valence band satellite structure we will consider the cluster CuCI~-. The emission from the fully occupied valence levels and from the partly filled valence level b, will be treated separately. For emission f~§m bl the spin must be taken into account explicl~ly, because of the Pauli exclusion principle. a). Final state holes in two levels of different syrm~etry: After emission of an electron from one of the full valence levels with b~ , e or a symmetry, there are four z .1 f . dz~fer§nt fln~l states ~n posslble: u
According to Table ; the cross-section for p emission in the He I excited CuCI 2 valence band is 7 times larger than that for d emission, whereas in the He II and AI K~ spectra the crosssection for d emission is slightly larger. As seen from Fig. ; the p emission in the main band is mainly within the energy region of 4 to 8 eV, and the d emission is between 3 and 6 eV. The center of gravity for the p emission is at 6 eV as seen from the He I spectrum. Because the p/d cross-section ratios in He II and AI K~ are comparable in size, the experimental energy positions and intensities can be compared (Table 2).
Peak
,
energy A1K~ 4.8 11.2 13.0 13.7
(eV) the is
Intensity He I I A1K~ 0.87 0.04 0.04 0.05
0.93 }
0.02 0.05
The intensity of the 3d 8 multiplet is found to be 0.13 and 0.07 for He II and AI K~, respectively (Table 2). If the sudden approximation is released, as is expected at low kinetic energies, the adiabatic peak gains intensity. In that case the 3d 8 peaks would have a lower intensity in UPS than in XPS. Because this is not the case, we find evidence that the sudden approximation is valid for He II, and that its breakdown will be at lower kinetic energy. Comparing the valence band spectra with the core spectra of CuCI 2 [6], it is immediately clear that the satellite intensity is much smaller in the valence band than in the core hole emission. The intensity of the 2p core hole satellite is equal to 0.38. The CuCI~ structure has space group C~h. There is a d~storted octahedron of CI ato~N
f ~n = and]d2 + BnL|d2 + YndlL2 + 6nLIL2'
(2)
where the indices | and 2 in the Slater determinants indicate the initial b.Jg hole and the created photo-hole, respectively. The eigen values E and coefficients a , Bn, Tn and 6 can be ~ound from the secular n n equatlons and determinant: U-E
T]
T[
A[-E
T2
0
0
T2
T2
0
0
T2
A2-g T]
=0,
(3)
T] A]+A2-E
where the Coulomb repulsion U =, T = and A = E(L )-E(dl)~ q =I|~ 2. C~ulomb q interactions q betwee~ the ~igand valen c e electrons have been neglected, because these orbitals are not very localized• The intensities of the various states are equal to 2 In = [(Adan + ALTn)C°SQ
- (AdBn + AL&n)Sin@]
with Ad(e) = IAd(L)[exp(ik--~d(L))
,
(4)
where IA .... [ is the amplitude for emission of a d(L) and exp(ik-~d(e~) is a phase factor, where R .... is the ~e~l space position of the atom, a E ~ d ~ is the wave vector of the continuum electron in the final state. The total emission from a ~eparate occupied valence level is equal to IA•I L + IA_I 2. The sztuatlon of core ho~e emlsslon can be obtained by taking the limit T 2 ~ 0, which
ele~gn,
•
.
d
.
•
167
ELECTRON CORRELATION EFFECTS
Vol. 42, No. 3
means that the photo-hole is localized. b). Final state holes in two levels of the same symmetry. .b'L : For the emission• from the b g, the triplet flna~ states, having E = 0, are l equal to:
order to obtain the total intensity including the emission from extra non bonding ligand orbitals, we have to add 21A~I 2 for two remaining ligand electrons. Combining case a and b the intensities will be equal to:
~f(T) = d~e ~, HiL +, (d~L ~ - e~d+)/~2. + The d~L ~ state cannot be reached from b. . The intensity of the triplet states is equalgto:
' +d ++~n(d ' +L ++L + d t )/V2 + 6 n'L+L +. = and
T lV2
0
TIV2
AI-e
TIV2
0
T]~/2
2~1-~
(6)
=
0.
(7)
The emission is equal to !
I
= [AdQnCOS@ + Bn (ALCOSG - Adsin@) n V2 '
- AL6nSin@]
B'n cOS@ - 6 n'sin@) 2 (~-
14 = 1I/2[Adl2sin2@
The coefficients ~ , 8 and are obtained from • n n a secular d e t e r m l n a n t equal t~ U-g
Vf
n
(5)
The three singlet final states are mixed ~(S)
= 91Adl2(anCOS@ - Bn sinO) 2 +
+ 91ALl2
14 = 3/2 IAd 12 sin2@ + 3/2 IAL 12 cosm0 + + 3ALA d cos@ sine.
!
I
2
.
(8)
The total emission from singlet and triplet final states together is proportional to the number of electrons initially present in the blg state: IAd]2+]ALlZ+IAdsin@ + ALCOSel 2 Evaluation: The intensities of the satellites can be calculated numerically. However there are many parameters in Eq.(3), so we will consider some approximations. First we consider the situation U>>T, in which the low kinetic energy satellite has pure dd final state character (~=~'=l). The total intensity of this satellite is equal to 91Ad 12 cos20, and proportional to the amount of d character in the initial state. However, the neglect of T is not realistic. A better approximation is to take in Eq.(3) Tt~is= TI and A2 = A| for. all valence states. In case a non bonding final state ~4=-Y4=]/~2 is obtained, with an intensity 14 = ½(Ad sin@ + A L cos@) 2
(9)
The remaining 3 x 3 determinant becomes equal to Eq.(7) and the intensities are given by Eq.(8). For the employed radiation sources the interference terms between the d and p emission can be neglected. Due to the averaging of the phase factors (Eq.4) over all orientations of the cluster the interference terms are small if kR -- 2z, where R = IRI - R2[ is the lnteratomlc distance, and the wave vecEor k of the continuum electron is given by k(~ -I) ~ 0.5~E (eV). For obtaining the total intensities, all valence levels have to be included. In the expressions for the hybridization each Cu 3d orbital interacts with one linear combination of ligand orbitals. Each of these contains 2 electrons, so that so far only lO of the 12 ligand electrons has been taken into account. Therefore, in
+
ll/21ALI2COS2@ ,
.
Itotal=IAdl2(9+sin2@)+IALl2(l]+cos2@)
(10)
The 3dS-like satellite intensity can be calculated, if the initial state wave function coefficients are known. From the evaluation of the core hole emission we obtained approximately cos2@ = 0.6 and T] = 2 eV [6]. From Table 2 the experimental value for the average distance between main peak and satellite in the valence band is found to be 7.6 eV. In the evaluation of Eq.(7) this value is obtained for U = 6.70 eV, which agrees with the results obtained from the L^M,.M.. Auger: 5 < U < 7 eV [6]. The coefficients for the 3dB-like satellite are found to be =; = 0.880, 8: = 0.43] and 6: = 0.20]. Taking in mq.{lO) lOIAdl2=~= a~d 6]ATI2=OL , where o. and o e are theUatomic cross-sEctions from Table ], we obtain the results given in Table 3 for the intensity of the 3dB-like satellite. Table source He I He I I A1 Ks
3.
3dB-like s a t e l l i t e theory 0.03 0.14 0.13
intensity. experiment ~ 0 0.13 0.07
At the top of Fig. 3 we have indicated for the 3dB-like satellite the relative energy positions calculated using the atomic Slater integrals from Mann [9], and the intensities taken proportional to the multiplicities. This is only exact in the limit U>>T, and not when the 3dB-like state is hybridized with the other final states. Because in CuCI9 the satellite • • malnly • is 3d 8 (5], = 0.88), we expeEt the atomic multipletsplitting to be a good first approximation. In contrast with the 3dS-like final state, which is localized at the Cu site, the intensities and energy positions of the other final states cannot be determined, without taking the crystal potential into account. In the crystal these states have additional interactions and are mixed into a broad band, which is experimentally observed between 3 and 8 eV (Fig. l). The p emission corresponds to the final states LIL~ and dlL2, and the d emission to the • z final states L.d^ and d.d^. z Because these states are strongly mlxld in t~e region of the main band, they are difficult to disentangle. From Fig. ] is seen that the top of the valence band gives mainly d-emission. This energy region will have mainly Lid 2 final states, because the did 2
168
ELECTRON CORRELATION EFFECTS
Vol. 42, No. 3
3F
3p
L.ol ,P. ool
~G
"~ 0,6 -I" 3 0 4 ~3 12
o~-
--~:' Photon energy
Fig. 4. R e s o n a n t p h o t o e m i s s i o n
from e m i s s i o n of the v a r i o u s states as a p h o t o n energy r e l a t i v e to r e s o n a n c e lated w i t h T = 2 eV, cos20 = 0.6, F
z
10
12 BINDING
14 ENERGY
(eV)
3. The He I I e x c i t e d v a l e n c e b a n d e m i s s i o n b e t w e e n 10 and 15 eV b i n d i n g e n e r g y . The t e r m splitting and t h e m u l t i p l i c i t i e s by the positions and t h e h e i g h t s the top of the figure.
are indicated of the bars at
states have a too high correlation energy. Resonant photoemission, as discovered by Guillot at al. [I0] in nickel metal using synchrotron radiation, can give a strong enhancement of the 3d 8 satellite in tile Cu dihalides. Besides the off-resonance excitation as discussed so far there are other channels to a 3d ° final state. At resonance, the excitation 3p-*3d followed by a simultaneous super-Coster-Kronig (sCK) decay creates the same final state: 3p63d 9 + h~ 0 ~ 3pS3d l ° ~ 3p63d s + e- . The resonance energy h~ 0 is about 72 eV. Because no resonant photoemission is expected from the 3p63dl°L initial state, the satellite intensities are given by (Davis and Feldkamp [|I ])
= I ~ ~÷q cos0 ~
~n~ sin012
V~
'
with e = (hv - hv0)/F,
(II) 2 . where h~ is the photon energy, 2F = 2~V ~, is the sCK decay width (FWHH), and the Faro a s ~ e t r y parameter < 3di~13 p > q = (12) ~Vsc K < g ~ [ ~ t 3 d
CuCI_. The d f u n c t i o n of are calcu-
= 1 eV, q = 1.5, ~ = 0.880, ~ = 0.431, ~ = -0.400, ~ = 0 . 4 4 3 7 ~ l = - 0 . 2 5 7 and ~ = 0 . 7 8 6 . I (Thick line) ~s the i n t e n s i t y of the 3 d S - { i k e final state. 12 and I_ are the i n t e n s i t i e s of the
Fig.
n
(eV)
>
The intensity 14 does not change. The p-emission has been omitted, because it does not depend on
states c o r r e s p o n d i n g ~o the m a i n band. The c o n s t a n t i n t e n s i t y of the non b o n d i n g final (I 4 = 0.234) has not b e e n drawn.
state
the photon energy. For I the p-emission is only 5 percent of the total o~f-resonance emission. The d emission of the various final states has been calculated as a function of the photon energy (Fig. 4), using the initial state coefficients obtained from core hole emission and the final state coefficients obtained from off-resonant photo-emission. Thus, according to these calculations, a strong enhancement of the photoemission at resonance for the 3de-like satellite is expected. Conclusions: Due to the correlation in the final state, the holes tend to move to opposite atoms, in order to lower their energy with an amount U - A. The rate of this process depends on the response time of the medium, which is proportional to the inverse of the effective transfer integral in the final state [12]. This effective transfer integral, equal to T for core hole emission will be equal to T~2 in the case of valence band emission, because both the initial hole and the created photo-hole can hop to the ligand site. This results in a strong reduction of the satellite intensity, at least if 0
REFERENCES |. 2. 3. 4.
5. 6. 7.
S.F. Alvarado, M. Erbudak and P. Munz, Phys. Rev. B 14, 2740 (1976). C.S. Fadley and D.A. Shirley, Phys. Rev. Lett. 21, 980 (1968). E.K. Li, K.H. Johnson, D.E. Eastman and J.L. Freeouf, Phys. Rev. Lett. 32, 470 (1974). H. van der Heide, R. Hemmel. C.F. van Bruggen and C. Haas, J. Solid State Chem. 33, 17 (1980). D.---R.Penn, Phys. Rev. Lett. 42, 921 (1979). G. van der Laan, C. Westra, ~ . Haas and G.A. Sawatzky, Phys. Rev. B 23, 4369 (1981). A. Goldmann, J. Tejeda, N.J. Shevchik and M. Cardona, Phys. Rev. B IO, 4388 (1974).
8.
J.H. Scofield, J. Electron Spectrosc. Relat. Phenom. 8, 129 (1976). 9. J.B. Mann, Los Alames Scientific Laboratory Report No LASL-3690 (1967) (unpublished). I0. C. Guillot, Y. Ballu, J. Paign@, J. Lecante, K.P. Jain, P. Thiry, R. Pinchaux, Y. P~troff and L.M. Falicov, Phys. Rev. Lett. 39, 1632 (1977). 11. L.C. Davis and L.A. Feldkamp, Phys. Rev. B 23, 6239 (1981); L.C. Davis, to be published (]982). 12. G.A. Sawatzky and A. Lenselink, J. Chem. Phys. 7_22, 3748 (1980).
Solid State Communications, Printed in Great Britain.
Voi.42, No.3, pp.165-168,
ELECTRON CORRELATION EFFECTS
1982.
0038-1098/82/150165-04503.00/0 Pergamon Press Ltd.
IN THE VALENCE BAND PHOTOEMISSION
SPECTRA OF COPPER DICHLORIDE
Gerrit van der Laan Laboratory
of Inorganic Chemistry and Laboratory of Physical Chemistry, The University of Groningen, Nijenborgh 16, 9747 AG Groningen, The Netherlands. ( Received 8 December
1981 by A.R. Miedema )
He I, He II and AI K~ photoemission measurements of the valence band of CuCI 2 are reported. The presence of the 3dS-like satellite indicates the strong correlation effects in the final state and the breakdown of the one-particle model. It is shown that the reduction of the satellite intensity in the valence band compared with the core hole emission is caused by the delocalization of the photo-hole. The satellite intensity in resonance with the super-Coster-Kronig decay is calculated.
The valence band photoemission spectra of compounds with initially full valence bands can be interpreted with a one-particle density of states (DOS) model. Also for compounds with partly filled valence bands, but with negligible Coulomb interactions between the final state holes, the spectrum reflects the DOS. Several authors have attempted to interpret in the same way the UPS and XPS valence band spectra of compounds, in which large Coulomb interactions are present between the final state holes. Some examples for this are Fe304 [I], Fe, Co and Ni [2] and the 3d transition metal pyrites [3,4]. However, we think that the valence band spectra of these compounds cannot be described adequately within a one-particle model. Penn [5] has outlined this already for the Ni valence band. The presence of a 3d -like satellite is clear evidence for the breakdown of the one-particle model in CuCI 2. In a previous paper [6] we have shown that the core hole emission spectra of Cu dihalides could be explained with a model, which takes into account the strong Coulomb interaction between the final state holes. In this paper this model is extended to the case of valence band emission and the results are compared with UPS and XPS measurements. To our knowledge there are no UPS reports on solid CuCI 2 in the literature. The compound is very hygroscopic and it slowly decomposes into monohalide and halogen gas. The powdered material charges inhomogeneously during the photo-ionization process. This results in a low counting rate and a severe line broadening, especially at low kinetic energies as in UPS. We managed to avoid these charging effects by preparing a thin film. For this purpose purified CuCI 2 was dissolved in a mixture of ethanol and acetone (I:I). In a nitrogen atmosphere a degreased Cu metal substrate was spread with a thin film of this solution, and the solvent was evaporated. Under the exclusion of air the sample was inserted into a VG ADES 400 spectrometer, and the remaining thin film was checked for its composition with XPS. Only very weak carbon and oxygen lines were observed, and the Cu core spectra had the proper satellite
structure of CuCI_. The UPS and XPS spectra are given in Fig.71 and Fig. 2, respectively. The Fermi level of the Cu metal substrate has been taken as the zero binding energy reference. The UPS spectra have not been corrected for background and analyzer transmission. The transmission is inversely proportional to the kinetic energy. This gives raise to the large increase in the intensity for He I at higher binding energies. The small peaks at 2.5 and 3.0 eV may be due to small amounts of CuCI, caused by the decomposition of the dihalide at the
i
/HeZ
.
j 0
rr
'
i
,
4
I
,
8
Binding energy F i g . 1 . He I a n d He I I emission f r o m CuC12.
I
12
(eV)
excited
valence
band
surface. In the AI Ks and He II spectra a 3d 8like final state is observed. In the He I spectrum this structure could not be resolved because of the small Cu 3d cross-section at this energy. Table 1. Atomic cross-section ratios of C1 3p a n d Cu 3d a s g i v e n b y G o l d m a n n e t and S c o f i e l d [8]. Radiation He I He I I A1 KS
165
source
0(C1
the al.
3p6)/O(Cu 3.50 0.30 0.41
[7]
3d 1 ° )
Vol• 42, No. 3
ELECTRON CORRELATION EFFECTS
166
around the Cu with 4 C1 at a distance 2.30 and 2 C1 at 2.95 ~. The local crystal field at the Cu site has approximately D4h sym~netry. The 3d orbitals with b 2 and e symmetry of a particular Cu atom ar§ hybridized with linear combinations of p~-type orbitals of the neighbouring CI atoms with b 2 and e symmetry. The 3d orbitals with a. gand b, g symmetry are hybridized with linearJ§ombina~ons of pO-type orbitals with a! and b] syn~netry. In the g~ound state onegeleetro~ is missing in the b~ . Working with holes, rather than with ei§ctrons, the ground state wave function can be written as
CI 3s
~g = b ~]g = d+cosO - Lisin@ L
8 12 Binding energy (eV) F i g . 2 . A1 K~ e x c i t e d f r o m CuC12 .
valence
16
20
band emission
T a b l e 2 . The e x p e r i m e n t a l energy positions and i n t e n s i t i e s for the peaks observed in v a l e n c e b a n d o f CuC12. T h e t o t a l intensity normalized to one.
main band 3d 8 3d 8 3d s
3F iD,3p IG
Binding He I I 5.0 11.2 13.0 13.7
(I)
where d and L are metal d and ligand p orbitals, respectively, and the parameter cos@ describes the covalent mixing. We assume that metal d and ligand p orbitals are orthogonal. For the evaluation of the valence band satellite structure we will consider the cluster CuCI~-. The emission from the fully occupied valence levels and from the partly filled valence level b, will be treated separately. For emission f~§m bl the spin must be taken into account explicl~ly, because of the Pauli exclusion principle. a). Final state holes in two levels of different syrm~etry: After emission of an electron from one of the full valence levels with b~ , e or a symmetry, there are four z .1 f . dz~fer§nt fln~l states ~n posslble: u
According to Table ; the cross-section for p emission in the He I excited CuCI 2 valence band is 7 times larger than that for d emission, whereas in the He II and AI K~ spectra the crosssection for d emission is slightly larger. As seen from Fig. ; the p emission in the main band is mainly within the energy region of 4 to 8 eV, and the d emission is between 3 and 6 eV. The center of gravity for the p emission is at 6 eV as seen from the He I spectrum. Because the p/d cross-section ratios in He II and AI K~ are comparable in size, the experimental energy positions and intensities can be compared (Table 2).
Peak
,
energy A1K~ 4.8 11.2 13.0 13.7
(eV) the is
Intensity He I I A1K~ 0.87 0.04 0.04 0.05
0.93 }
0.02 0.05
The intensity of the 3d 8 multiplet is found to be 0.13 and 0.07 for He II and AI K~, respectively (Table 2). If the sudden approximation is released, as is expected at low kinetic energies, the adiabatic peak gains intensity. In that case the 3d 8 peaks would have a lower intensity in UPS than in XPS. Because this is not the case, we find evidence that the sudden approximation is valid for He II, and that its breakdown will be at lower kinetic energy. Comparing the valence band spectra with the core spectra of CuCI 2 [6], it is immediately clear that the satellite intensity is much smaller in the valence band than in the core hole emission. The intensity of the 2p core hole satellite is equal to 0.38. The CuCI~ structure has space group C~h. There is a d~storted octahedron of CI ato~N
f ~n = and]d2 + BnL|d2 + YndlL2 + 6nLIL2'
(2)
where the indices | and 2 in the Slater determinants indicate the initial b.Jg hole and the created photo-hole, respectively. The eigen values E and coefficients a , Bn, Tn and 6 can be ~ound from the secular n n equatlons and determinant: U-E
T]
T[
A[-E
T2
0
0
T2
T2
0
0
T2
A2-g T]
=0,
(3)
T] A]+A2-E
where the Coulomb repulsion U =
- (AdBn + AL&n)Sin@]
with Ad(e) = IAd(L)[exp(ik--~d(L))
,
(4)
where IA .... [ is the amplitude for emission of a d(L) and exp(ik-~d(e~) is a phase factor, where R .... is the ~e~l space position of the atom, a E ~ d ~ is the wave vector of the continuum electron in the final state. The total emission from a ~eparate occupied valence level is equal to IA•I L + IA_I 2. The sztuatlon of core ho~e emlsslon can be obtained by taking the limit T 2 ~ 0, which
ele~gn,
•
.
d
.
•
167
ELECTRON CORRELATION EFFECTS
Vol. 42, No. 3
means that the photo-hole is localized. b). Final state holes in two levels of the same symmetry. .b'L : For the emission• from the b g, the triplet flna~ states, having E = 0, are l equal to:
order to obtain the total intensity including the emission from extra non bonding ligand orbitals, we have to add 21A~I 2 for two remaining ligand electrons. Combining case a and b the intensities will be equal to:
~f(T) = d~e ~, HiL +, (d~L ~ - e~d+)/~2. + The d~L ~ state cannot be reached from b. . The intensity of the triplet states is equalgto:
' +d ++~n(d ' +L ++L + d t )/V2 + 6 n'L+L +. = and
T lV2
0
TIV2
AI-e
TIV2
0
T]~/2
2~1-~
(6)
=
0.
(7)
The emission is equal to !
I
= [AdQnCOS@ + Bn (ALCOSG - Adsin@) n V2 '
- AL6nSin@]
B'n cOS@ - 6 n'sin@) 2 (~-
14 = 1I/2[Adl2sin2@
The coefficients ~ , 8 and are obtained from • n n a secular d e t e r m l n a n t equal t~ U-g
Vf
n
(5)
The three singlet final states are mixed ~(S)
= 91Adl2(anCOS@ - Bn sinO) 2 +
+ 91ALl2
14 = 3/2 IAd 12 sin2@ + 3/2 IAL 12 cosm0 + + 3ALA d cos@ sine.
!
I
2
.
(8)
The total emission from singlet and triplet final states together is proportional to the number of electrons initially present in the blg state: IAd]2+]ALlZ+IAdsin@ + ALCOSel 2 Evaluation: The intensities of the satellites can be calculated numerically. However there are many parameters in Eq.(3), so we will consider some approximations. First we consider the situation U>>T, in which the low kinetic energy satellite has pure dd final state character (~=~'=l). The total intensity of this satellite is equal to 91Ad 12 cos20, and proportional to the amount of d character in the initial state. However, the neglect of T is not realistic. A better approximation is to take in Eq.(3) Tt~is= TI and A2 = A| for. all valence states. In case a non bonding final state ~4=-Y4=]/~2 is obtained, with an intensity 14 = ½(Ad sin@ + A L cos@) 2
(9)
The remaining 3 x 3 determinant becomes equal to Eq.(7) and the intensities are given by Eq.(8). For the employed radiation sources the interference terms between the d and p emission can be neglected. Due to the averaging of the phase factors (Eq.4) over all orientations of the cluster the interference terms are small if kR -- 2z, where R = IRI - R2[ is the lnteratomlc distance, and the wave vecEor k of the continuum electron is given by k(~ -I) ~ 0.5~E (eV). For obtaining the total intensities, all valence levels have to be included. In the expressions for the hybridization each Cu 3d orbital interacts with one linear combination of ligand orbitals. Each of these contains 2 electrons, so that so far only lO of the 12 ligand electrons has been taken into account. Therefore, in
+
ll/21ALI2COS2@ ,
.
Itotal=IAdl2(9+sin2@)+IALl2(l]+cos2@)
(10)
The 3dS-like satellite intensity can be calculated, if the initial state wave function coefficients are known. From the evaluation of the core hole emission we obtained approximately cos2@ = 0.6 and T] = 2 eV [6]. From Table 2 the experimental value for the average distance between main peak and satellite in the valence band is found to be 7.6 eV. In the evaluation of Eq.(7) this value is obtained for U = 6.70 eV, which agrees with the results obtained from the L^M,.M.. Auger: 5 < U < 7 eV [6]. The coefficients for the 3dB-like satellite are found to be =; = 0.880, 8: = 0.43] and 6: = 0.20]. Taking in mq.{lO) lOIAdl2=~= a~d 6]ATI2=OL , where o. and o e are theUatomic cross-sEctions from Table ], we obtain the results given in Table 3 for the intensity of the 3dB-like satellite. Table source He I He I I A1 Ks
3.
3dB-like s a t e l l i t e theory 0.03 0.14 0.13
intensity. experiment ~ 0 0.13 0.07
At the top of Fig. 3 we have indicated for the 3dB-like satellite the relative energy positions calculated using the atomic Slater integrals from Mann [9], and the intensities taken proportional to the multiplicities. This is only exact in the limit U>>T, and not when the 3dB-like state is hybridized with the other final states. Because in CuCI9 the satellite • • malnly • is 3d 8 (5], = 0.88), we expeEt the atomic multipletsplitting to be a good first approximation. In contrast with the 3dS-like final state, which is localized at the Cu site, the intensities and energy positions of the other final states cannot be determined, without taking the crystal potential into account. In the crystal these states have additional interactions and are mixed into a broad band, which is experimentally observed between 3 and 8 eV (Fig. l). The p emission corresponds to the final states LIL~ and dlL2, and the d emission to the • z final states L.d^ and d.d^. z Because these states are strongly mlxld in t~e region of the main band, they are difficult to disentangle. From Fig. ] is seen that the top of the valence band gives mainly d-emission. This energy region will have mainly Lid 2 final states, because the did 2
168
ELECTRON CORRELATION EFFECTS
Vol. 42, No. 3
3F
3p
L.ol ,P. ool
~G
"~ 0,6 -I" 3 0 4 ~3 12
o~-
--~:' Photon energy
Fig. 4. R e s o n a n t p h o t o e m i s s i o n
from e m i s s i o n of the v a r i o u s states as a p h o t o n energy r e l a t i v e to r e s o n a n c e lated w i t h T = 2 eV, cos20 = 0.6, F
z
10
12 BINDING
14 ENERGY
(eV)
3. The He I I e x c i t e d v a l e n c e b a n d e m i s s i o n b e t w e e n 10 and 15 eV b i n d i n g e n e r g y . The t e r m splitting and t h e m u l t i p l i c i t i e s by the positions and t h e h e i g h t s the top of the figure.
are indicated of the bars at
states have a too high correlation energy. Resonant photoemission, as discovered by Guillot at al. [I0] in nickel metal using synchrotron radiation, can give a strong enhancement of the 3d 8 satellite in tile Cu dihalides. Besides the off-resonance excitation as discussed so far there are other channels to a 3d ° final state. At resonance, the excitation 3p-*3d followed by a simultaneous super-Coster-Kronig (sCK) decay creates the same final state: 3p63d 9 + h~ 0 ~ 3pS3d l ° ~ 3p63d s + e- . The resonance energy h~ 0 is about 72 eV. Because no resonant photoemission is expected from the 3p63dl°L initial state, the satellite intensities are given by (Davis and Feldkamp [|I ])
= I ~ ~÷q cos0 ~
~n~ sin012
V~
'
with e = (hv - hv0)/F,
(II) 2 . where h~ is the photon energy, 2F = 2~V ~, is the sCK decay width (FWHH), and the Faro a s ~ e t r y parameter < 3di~13 p > q = (12) ~Vsc K < g ~ [ ~ t 3 d
CuCI_. The d f u n c t i o n of are calcu-
= 1 eV, q = 1.5, ~ = 0.880, ~ = 0.431, ~ = -0.400, ~ = 0 . 4 4 3 7 ~ l = - 0 . 2 5 7 and ~ = 0 . 7 8 6 . I (Thick line) ~s the i n t e n s i t y of the 3 d S - { i k e final state. 12 and I_ are the i n t e n s i t i e s of the
Fig.
n
(eV)
>
The intensity 14 does not change. The p-emission has been omitted, because it does not depend on
states c o r r e s p o n d i n g ~o the m a i n band. The c o n s t a n t i n t e n s i t y of the non b o n d i n g final (I 4 = 0.234) has not b e e n drawn.
state
the photon energy. For I the p-emission is only 5 percent of the total o~f-resonance emission. The d emission of the various final states has been calculated as a function of the photon energy (Fig. 4), using the initial state coefficients obtained from core hole emission and the final state coefficients obtained from off-resonant photo-emission. Thus, according to these calculations, a strong enhancement of the photoemission at resonance for the 3de-like satellite is expected. Conclusions: Due to the correlation in the final state, the holes tend to move to opposite atoms, in order to lower their energy with an amount U - A. The rate of this process depends on the response time of the medium, which is proportional to the inverse of the effective transfer integral in the final state [12]. This effective transfer integral, equal to T for core hole emission will be equal to T~2 in the case of valence band emission, because both the initial hole and the created photo-hole can hop to the ligand site. This results in a strong reduction of the satellite intensity, at least if 0
REFERENCES |. 2. 3. 4.
5. 6. 7.
S.F. Alvarado, M. Erbudak and P. Munz, Phys. Rev. B 14, 2740 (1976). C.S. Fadley and D.A. Shirley, Phys. Rev. Lett. 21, 980 (1968). E.K. Li, K.H. Johnson, D.E. Eastman and J.L. Freeouf, Phys. Rev. Lett. 32, 470 (1974). H. van der Heide, R. Hemmel. C.F. van Bruggen and C. Haas, J. Solid State Chem. 33, 17 (1980). D.---R.Penn, Phys. Rev. Lett. 42, 921 (1979). G. van der Laan, C. Westra, ~ . Haas and G.A. Sawatzky, Phys. Rev. B 23, 4369 (1981). A. Goldmann, J. Tejeda, N.J. Shevchik and M. Cardona, Phys. Rev. B IO, 4388 (1974).
8.
J.H. Scofield, J. Electron Spectrosc. Relat. Phenom. 8, 129 (1976). 9. J.B. Mann, Los Alames Scientific Laboratory Report No LASL-3690 (1967) (unpublished). I0. C. Guillot, Y. Ballu, J. Paign@, J. Lecante, K.P. Jain, P. Thiry, R. Pinchaux, Y. P~troff and L.M. Falicov, Phys. Rev. Lett. 39, 1632 (1977). 11. L.C. Davis and L.A. Feldkamp, Phys. Rev. B 23, 6239 (1981); L.C. Davis, to be published (]982). 12. G.A. Sawatzky and A. Lenselink, J. Chem. Phys. 7_22, 3748 (1980).