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Graphite intercalation compounds charge transfer from auger spectroscopy measurements
Synthetic Metals, 8 ( 1 9 8 3 ) 125 - 130
125
G R A P H I T E I N T E R C A L A T I O N COMPOUNDS CHARGE FROM A U G E R SPECTROSCOPY MEASUREMENTS
TRANSFER
D. M A R C H A N D , C. F R E T I G N Y , M. L A G U E S a n d A. P. L E G R A N D
Laboratoire de Physique Quantique, E,R.A. 676, E.S.P.C.I., I0 rue Vauquelin. 75231 Paris Cddex 05 (France)
Summary The shape of the Carbon K.V.V. Auger transition in graphite intercalation c o m p o u n d s is n o t yet clearly understood. We present here a new analysis of the spectra, which takes into account the experimental spectrum of pure graphite. Previously proposed descriptions are inconsistent with this detailed analysis. Cross Auger transitions involving non-transferred electrons of the donor atom, and a carbon K hole seem to be consistent with experiment. This leads to charge transfers of 0.72 for CsCs and 0.96 for CSC24, both synthesized under ultra-high vacuum.
Introduction The K.V.V. Auger line-shape of a solid is basically related to the valence band density of states (D.O.S.) of the material studied [1 - 6]. Different workers analysed Auger transitions from graphite intercalation c o m p o u n d s (GICs), in order to describe the conduction band, especially for donor-type GICs [7 - 12]. Nevertheless, the proposed models failed to explain the amplitude of the Fermi level peak: in the case of stage 1, the observed peak is an order of magnitude more intense than predicted [9 - 12]. We thus used a different method, which takes into account the fact that the major part of the K.V.V. transition of a GIC is due to graphite. Recalling briefly the basis underlying most analyses, the Lander's model, we present our description, and then compare it with experimental spectra of CsCn.
The Lander's model According to Lander's description [ 1], the K.V.V. Auger line shape I(E) is simply the sum over all possible transitions leading to the final state energy, E. Moreover, assuming negligible matrix element effects, the transition rate 0379-6779]83]$3.00
© Elsevier S e q u o i a ] P r i n t e d in T h e N e t h e r l a n d s
126 for each definite initial energy is simply proportional to the valence band D.O.S. n(E1) and n(E2) of both involved electrons:
I(E) ~ fn(E,)n(E2) dE,
(1)
with: E, +E2 = E +EK (hole)
(2)
If the energy reference is taken at the hole level, E K = 0, I ( E ) is the selfconvolution of n(E): I(E) ~ fn(x)n(E --x) dx = n*n
(3)
This extremely simple description is valid only over very specific limits. First of all, the Auger transition should n o t be localized and should involve ,the true band structure, with negligible potential effects of the hole [13]. More generally, the screening of the initial hole must be negligible and slow compared with the Auger transition rate [14, 15]. A second limitation is the influence of matrix elements: this may alter the line shape, b u t it may be accounted for by including transition probabilities in eqn. (3). Finally, Lander's description assumes direct emission of the Auger electrons in the vacuum: in fact, transport through the material produces a convolution of the spectrum with a loss-function aCE): I(E) ~ a*n*n
(4)
The conditions of' nonlocalization, weak screening, and weak interaction between the holes seem to be verified for graphite [8]. The loss-function, however, is quite important. This effect may be corrected by measuring directly the energy distribution of secondary electrons, using a primary-beam energy in the range of the Auger transition. The proper Auger line shape is obtained by deconvolution of the experimental spectrum [ 8]. Nevertheless, eqn. (4) accounts correctly for the K.V.V. transition of graphite. Our basic assumption for the present analysis is thus the validity of Lander's description, as it was assumed by the other teams in studying the GICs K.V.V. transition [9, 12].
Narrow difference model The basic point here is that n(E), the density of states of a GIC, is the sum of the graphite density of states g ( E ) (shifted in reference to the Fermi level), and of a narrow part p i E ) induced by intercalation. Following Lander's model: I(E) ~ g*g + 2g*p + p *p
(5)
127 where g . g = G(E) is the K.V.V. line shape of pure graphite. Thus, it seems possible to simplify the analysis of I(E) by subtracting the experimental Auger spectrum of graphite. Considering the base widths D = 22 eV of g(E) and d = 1 eV of p(E), the base widths of the three contributions are, respectively, about 44 eV for g . g , 23 eV f o r g * p and 2 eV f o r p . p . It must be pointed o u t that I(E) = G(E) within an energy range extending over about 20 eV (E < 260 eV), while parts (b) and (c) both cancel. This allows us, in principle, to work out the subtraction with the proper amplitude and background. Part (b) is the graphite D.O.S., slightly broadened by convolution with p; as (b) is also the major contribution to (I(E) -- G(E)) the comparison of its shape with the D.O.S. of graphite would be a qualitative check for the validity of the proposed analysis. If we assume that the integral of g is proportional to the number of valence electrons of graphite (four per carbon atom), and that the integral of p is proportional to the transferred charge q per carbon atom, we may define two ratios, T and S, proportional to the integrals of (b) and (c): T =
f2g,p dE/fg,g dE = q / 2
S = fp*p
dE/fg*g
dE = q2/16
(6) (7)
Results
The samples were synthesized under ultra-high vacuum, the Auger spectrum being recorded during the cesium deposition on the HOPG (highly oriented pyrolytic graphite) or single crystal graphite substrate [7]. Figure 1 (a) presents the Auger spectra of nearly pure CSC24, and (b) CsCs, compared with the spectrum of graphite. The line shape obtained after subtraction is presented in each case ((c) and (d)), compared with the density of states of graphite proposed by Murday et al. [ 11], on the basis of X-ray photoemission and X-ray emission spectroscopy measurements [16]. After subtraction of the narrow peak, the agreement between the obtained spectra and the D.O.S. of graphite is fairly good in both cases. This first check of the proposed description seems to be fairly positive. A second verification is based on eqns. (6) and (7): the areas of the two contributions T and S must be related T 2 = 4S
(8)
Both quantities were estimated precisely for more than twenty samples of various compositions. The results are presented in Fig. 2: the dashed line refers to eqn. (8). There is a clear disagreement between experiment and the self-convolution model (T 2 = 4S): for T = 0.04, S is a b o u t ten times more important than predicted by eqn. (8).
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Fig. 1. (a) Derivative of Auger line shape d/dE [E.I(E)] of C8C24 ( ) compared with the same spectrum for graphite ( . . . . ); (b) derivative of Auger line shape of CsC8; (c) difference b e t w e e n the spectrum I(E) of CSC24 and of graphite ( ), compared with the density of states of graphite as proposed by Murday et al. [ 1 1 ] ( . . . . ); (d) the same quantity for the c o m p o u n d CsCs.
The first conclusion is thus that no physical description relying only on the self-convolution could agree with experimental spectra. For instance, Murday e t al. [ 11] proposed that this important discrepancy could be due to screening of the hole by the surrounding atoms' electrons, which could add to the actual density of states for the K.V.V. transition. This could theoretically explain an increase in q in eqns. (6) and (7), but this cannot affect the basic relation between T and S. This is thus the first evidence that an Auger K.V.V. transition in GICs cannot be described by the self-convolution model alone. We therefore propose a model based on a cross Auger transition between the non-transferred charge (1 -- f) localized on the donor atom, and the K level hole of the twelve surrounding carbon atoms. This transition from elec-
129 6
r
i
=
n
5
•
•
u
°o
4
103.S 3 2 1
0
0.01
0.02
T
0.03
0.04
0.05
Fig. 2. T h e area r a t i o S o f t h e F e r m i level p e a k divided b y t h e g r a p h i t e p e a k area is p l o t t e d v s . t h e ratio T o f t h e cross t e r m (b) area (see t e x t ) t o the g r a p h i t e s p e c t r u m area. Acc o r d i n g to t h e s e l f - c o n v o l u t i o n m o d e l , t h e Auger s p e c t r a o f GICs s h o u l d o b e y t h e following law: T 2 = 4S ( . . . . ). P o i n t s (1) a n d (2) s h o w t h e p o s i t i o n o f stages 1 a n d 2, respectively.
trons near the Fermi level adds to the quantity S of eqn. (7), while the value of T = q / 2 is unchanged: S = [q2 + k (1 _ f ) 2 ] /16
(9)
where the fraction k of carbon atoms directly bounded to a donor atom is equal to 3/4 for stage 1, and to 1/2 otherwise. With the set of experimental points (Fig. 2) the corresponding values of the charge transfer per donor atom f = q n , are, respectively: Stage 1 f = 0.72 + 0.02 Stage 2 f = 0.96 + 0.03 This is in agreement with generally accepted charge transfers for alkali metals. In the case of stage 2, the ratio S is about 1.5 × 10 -4 and thus the Fermi level peak is extremely weak, even on differential Auger spectra (Fig. l(a)). This is in disagreement with Auger measurements of Pfluger [17], who observed on different stages of alkali metals, that the amplitude of the Fermi level peak was roughly proportional to the inverse of the stage. It seems that the "surface stage" of the samples, measured over a depth of about three carbon layers, is completely different from the bulk stage at thermal equilibrium. We showed this through segregation experiments which lead in any case to a stage 1 in the first layers [7]. It is clear that the interaction of an intercalated layer with the surface could be sufficiently attractive to stabilize an average intercalated concentration completely different from the bulk composition. Conclusion We show in the present communication that previous descriptions of the Auger spectra of GICs, based on the self-convolution model, disagree
130
with the present analysis of experimental data. The proposed description, without any adjustable parameter, is in fair agreement with experimental data and leads to realistic charge transfer values. The use of Auger spectra, deconvoluted by the experimental loss function, should improve the present description. On the other hand, the quantities obtained after subtraction {Fig. l(c) and (d)) are so weak, that the unavoidable noise due to deconvolution could lead to a loss of accuracy. Further use of this analysis of experimental spectra, and check of the proposed physical description in different cases (for instance, acceptor GICs), could clearly improve the knowledge of the conduction band of graphite intercalation compounds.
References 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15 16 17
J . J . Lander, Phys. Rev., 91 (1953) 1382. W. M. Mularie and W. T. Peria, Surf. Sci., 26 (1970) 125. V. Martinez, J. Electron Spectrosc. Relat. Phenom., 17 (1979) 33. M. C. Munoz, V. Martinez, J. A. Tagle and J. L. Sacedon, Phys. Rev. Lett., 44 (1980) 814. F. Soria, V. Martinez, M. C. Munoz and J. L. Sacedon, Phys. Rev. B, 24 (1981) 6926. G. F. Amelio, Surf. Sci., 22 (1970) 301. M. Lagues, D. Marchand, C. Fretigny and A. P. Legrand, Physics o f Intercalation Compounds, Springer, Berlin, 1981, p. 49. 6 London Int. Carbon and Graphite Conf., Sept. 1982, p. 85. M. A. Smith and L. L. Levenson, Phys. Rev. B, 16 (1977) 2973. P. Oelhafen, P. Pfluger and H.- J. Giintherodt, Solid State Commun., 32 (1979) 885. P. Oelhafen, P. Pfluger, E. Hauser and H.- J. Giintherodt, Phys. Rev. Lett., 44 (1980) 197. J. S. Murday, B. I. Dunlap, F. L. Huston II and P. Oelhafen, Phys. Rev. B, 24 (1981) 4764. S. D. Bader, Solid State Commun., 35 (1980) 501. D. R. Jennison, Phys. Rev. Lett., 40 (1978) 807. G. A. Sawatzky and A. Lenselink, Phys. Rev. B, 21 (1980) 1790. G. Treglia, F. Ducastelle and D. Spanjaard, J. Phys. (Paris), 41 (1980) 281. F. R. McFeely, S. P. Kowalczyk, L. Ley, R. G. Cavell and D. A. Shirley, Phys. Rev. B, 9 (1974) 5268. P. Pfluger, personal communication.
125
G R A P H I T E I N T E R C A L A T I O N COMPOUNDS CHARGE FROM A U G E R SPECTROSCOPY MEASUREMENTS
TRANSFER
D. M A R C H A N D , C. F R E T I G N Y , M. L A G U E S a n d A. P. L E G R A N D
Laboratoire de Physique Quantique, E,R.A. 676, E.S.P.C.I., I0 rue Vauquelin. 75231 Paris Cddex 05 (France)
Summary The shape of the Carbon K.V.V. Auger transition in graphite intercalation c o m p o u n d s is n o t yet clearly understood. We present here a new analysis of the spectra, which takes into account the experimental spectrum of pure graphite. Previously proposed descriptions are inconsistent with this detailed analysis. Cross Auger transitions involving non-transferred electrons of the donor atom, and a carbon K hole seem to be consistent with experiment. This leads to charge transfers of 0.72 for CsCs and 0.96 for CSC24, both synthesized under ultra-high vacuum.
Introduction The K.V.V. Auger line-shape of a solid is basically related to the valence band density of states (D.O.S.) of the material studied [1 - 6]. Different workers analysed Auger transitions from graphite intercalation c o m p o u n d s (GICs), in order to describe the conduction band, especially for donor-type GICs [7 - 12]. Nevertheless, the proposed models failed to explain the amplitude of the Fermi level peak: in the case of stage 1, the observed peak is an order of magnitude more intense than predicted [9 - 12]. We thus used a different method, which takes into account the fact that the major part of the K.V.V. transition of a GIC is due to graphite. Recalling briefly the basis underlying most analyses, the Lander's model, we present our description, and then compare it with experimental spectra of CsCn.
The Lander's model According to Lander's description [ 1], the K.V.V. Auger line shape I(E) is simply the sum over all possible transitions leading to the final state energy, E. Moreover, assuming negligible matrix element effects, the transition rate 0379-6779]83]$3.00
© Elsevier S e q u o i a ] P r i n t e d in T h e N e t h e r l a n d s
126 for each definite initial energy is simply proportional to the valence band D.O.S. n(E1) and n(E2) of both involved electrons:
I(E) ~ fn(E,)n(E2) dE,
(1)
with: E, +E2 = E +EK (hole)
(2)
If the energy reference is taken at the hole level, E K = 0, I ( E ) is the selfconvolution of n(E): I(E) ~ fn(x)n(E --x) dx = n*n
(3)
This extremely simple description is valid only over very specific limits. First of all, the Auger transition should n o t be localized and should involve ,the true band structure, with negligible potential effects of the hole [13]. More generally, the screening of the initial hole must be negligible and slow compared with the Auger transition rate [14, 15]. A second limitation is the influence of matrix elements: this may alter the line shape, b u t it may be accounted for by including transition probabilities in eqn. (3). Finally, Lander's description assumes direct emission of the Auger electrons in the vacuum: in fact, transport through the material produces a convolution of the spectrum with a loss-function aCE): I(E) ~ a*n*n
(4)
The conditions of' nonlocalization, weak screening, and weak interaction between the holes seem to be verified for graphite [8]. The loss-function, however, is quite important. This effect may be corrected by measuring directly the energy distribution of secondary electrons, using a primary-beam energy in the range of the Auger transition. The proper Auger line shape is obtained by deconvolution of the experimental spectrum [ 8]. Nevertheless, eqn. (4) accounts correctly for the K.V.V. transition of graphite. Our basic assumption for the present analysis is thus the validity of Lander's description, as it was assumed by the other teams in studying the GICs K.V.V. transition [9, 12].
Narrow difference model The basic point here is that n(E), the density of states of a GIC, is the sum of the graphite density of states g ( E ) (shifted in reference to the Fermi level), and of a narrow part p i E ) induced by intercalation. Following Lander's model: I(E) ~ g*g + 2g*p + p *p
(5)
127 where g . g = G(E) is the K.V.V. line shape of pure graphite. Thus, it seems possible to simplify the analysis of I(E) by subtracting the experimental Auger spectrum of graphite. Considering the base widths D = 22 eV of g(E) and d = 1 eV of p(E), the base widths of the three contributions are, respectively, about 44 eV for g . g , 23 eV f o r g * p and 2 eV f o r p . p . It must be pointed o u t that I(E) = G(E) within an energy range extending over about 20 eV (E < 260 eV), while parts (b) and (c) both cancel. This allows us, in principle, to work out the subtraction with the proper amplitude and background. Part (b) is the graphite D.O.S., slightly broadened by convolution with p; as (b) is also the major contribution to (I(E) -- G(E)) the comparison of its shape with the D.O.S. of graphite would be a qualitative check for the validity of the proposed analysis. If we assume that the integral of g is proportional to the number of valence electrons of graphite (four per carbon atom), and that the integral of p is proportional to the transferred charge q per carbon atom, we may define two ratios, T and S, proportional to the integrals of (b) and (c): T =
f2g,p dE/fg,g dE = q / 2
S = fp*p
dE/fg*g
dE = q2/16
(6) (7)
Results
The samples were synthesized under ultra-high vacuum, the Auger spectrum being recorded during the cesium deposition on the HOPG (highly oriented pyrolytic graphite) or single crystal graphite substrate [7]. Figure 1 (a) presents the Auger spectra of nearly pure CSC24, and (b) CsCs, compared with the spectrum of graphite. The line shape obtained after subtraction is presented in each case ((c) and (d)), compared with the density of states of graphite proposed by Murday et al. [ 11], on the basis of X-ray photoemission and X-ray emission spectroscopy measurements [16]. After subtraction of the narrow peak, the agreement between the obtained spectra and the D.O.S. of graphite is fairly good in both cases. This first check of the proposed description seems to be fairly positive. A second verification is based on eqns. (6) and (7): the areas of the two contributions T and S must be related T 2 = 4S
(8)
Both quantities were estimated precisely for more than twenty samples of various compositions. The results are presented in Fig. 2: the dashed line refers to eqn. (8). There is a clear disagreement between experiment and the self-convolution model (T 2 = 4S): for T = 0.04, S is a b o u t ten times more important than predicted by eqn. (8).
128
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/'\
t~,,
I \\
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/ 11
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',
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I
240
250
(a)
260
Energy
270
280
290
(eV)
240
(b)
250
280
270
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Ener'~y (eV)
2go
II
t
I
/
c" t
'
t
f
/
'i
1
fk
(c)
r
~
i
(d)
Fig. 1. (a) Derivative of Auger line shape d/dE [E.I(E)] of C8C24 ( ) compared with the same spectrum for graphite ( . . . . ); (b) derivative of Auger line shape of CsC8; (c) difference b e t w e e n the spectrum I(E) of CSC24 and of graphite ( ), compared with the density of states of graphite as proposed by Murday et al. [ 1 1 ] ( . . . . ); (d) the same quantity for the c o m p o u n d CsCs.
The first conclusion is thus that no physical description relying only on the self-convolution could agree with experimental spectra. For instance, Murday e t al. [ 11] proposed that this important discrepancy could be due to screening of the hole by the surrounding atoms' electrons, which could add to the actual density of states for the K.V.V. transition. This could theoretically explain an increase in q in eqns. (6) and (7), but this cannot affect the basic relation between T and S. This is thus the first evidence that an Auger K.V.V. transition in GICs cannot be described by the self-convolution model alone. We therefore propose a model based on a cross Auger transition between the non-transferred charge (1 -- f) localized on the donor atom, and the K level hole of the twelve surrounding carbon atoms. This transition from elec-
129 6
r
i
=
n
5
•
•
u
°o
4
103.S 3 2 1
0
0.01
0.02
T
0.03
0.04
0.05
Fig. 2. T h e area r a t i o S o f t h e F e r m i level p e a k divided b y t h e g r a p h i t e p e a k area is p l o t t e d v s . t h e ratio T o f t h e cross t e r m (b) area (see t e x t ) t o the g r a p h i t e s p e c t r u m area. Acc o r d i n g to t h e s e l f - c o n v o l u t i o n m o d e l , t h e Auger s p e c t r a o f GICs s h o u l d o b e y t h e following law: T 2 = 4S ( . . . . ). P o i n t s (1) a n d (2) s h o w t h e p o s i t i o n o f stages 1 a n d 2, respectively.
trons near the Fermi level adds to the quantity S of eqn. (7), while the value of T = q / 2 is unchanged: S = [q2 + k (1 _ f ) 2 ] /16
(9)
where the fraction k of carbon atoms directly bounded to a donor atom is equal to 3/4 for stage 1, and to 1/2 otherwise. With the set of experimental points (Fig. 2) the corresponding values of the charge transfer per donor atom f = q n , are, respectively: Stage 1 f = 0.72 + 0.02 Stage 2 f = 0.96 + 0.03 This is in agreement with generally accepted charge transfers for alkali metals. In the case of stage 2, the ratio S is about 1.5 × 10 -4 and thus the Fermi level peak is extremely weak, even on differential Auger spectra (Fig. l(a)). This is in disagreement with Auger measurements of Pfluger [17], who observed on different stages of alkali metals, that the amplitude of the Fermi level peak was roughly proportional to the inverse of the stage. It seems that the "surface stage" of the samples, measured over a depth of about three carbon layers, is completely different from the bulk stage at thermal equilibrium. We showed this through segregation experiments which lead in any case to a stage 1 in the first layers [7]. It is clear that the interaction of an intercalated layer with the surface could be sufficiently attractive to stabilize an average intercalated concentration completely different from the bulk composition. Conclusion We show in the present communication that previous descriptions of the Auger spectra of GICs, based on the self-convolution model, disagree
130
with the present analysis of experimental data. The proposed description, without any adjustable parameter, is in fair agreement with experimental data and leads to realistic charge transfer values. The use of Auger spectra, deconvoluted by the experimental loss function, should improve the present description. On the other hand, the quantities obtained after subtraction {Fig. l(c) and (d)) are so weak, that the unavoidable noise due to deconvolution could lead to a loss of accuracy. Further use of this analysis of experimental spectra, and check of the proposed physical description in different cases (for instance, acceptor GICs), could clearly improve the knowledge of the conduction band of graphite intercalation compounds.
References 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15 16 17
J . J . Lander, Phys. Rev., 91 (1953) 1382. W. M. Mularie and W. T. Peria, Surf. Sci., 26 (1970) 125. V. Martinez, J. Electron Spectrosc. Relat. Phenom., 17 (1979) 33. M. C. Munoz, V. Martinez, J. A. Tagle and J. L. Sacedon, Phys. Rev. Lett., 44 (1980) 814. F. Soria, V. Martinez, M. C. Munoz and J. L. Sacedon, Phys. Rev. B, 24 (1981) 6926. G. F. Amelio, Surf. Sci., 22 (1970) 301. M. Lagues, D. Marchand, C. Fretigny and A. P. Legrand, Physics o f Intercalation Compounds, Springer, Berlin, 1981, p. 49. 6 London Int. Carbon and Graphite Conf., Sept. 1982, p. 85. M. A. Smith and L. L. Levenson, Phys. Rev. B, 16 (1977) 2973. P. Oelhafen, P. Pfluger and H.- J. Giintherodt, Solid State Commun., 32 (1979) 885. P. Oelhafen, P. Pfluger, E. Hauser and H.- J. Giintherodt, Phys. Rev. Lett., 44 (1980) 197. J. S. Murday, B. I. Dunlap, F. L. Huston II and P. Oelhafen, Phys. Rev. B, 24 (1981) 4764. S. D. Bader, Solid State Commun., 35 (1980) 501. D. R. Jennison, Phys. Rev. Lett., 40 (1978) 807. G. A. Sawatzky and A. Lenselink, Phys. Rev. B, 21 (1980) 1790. G. Treglia, F. Ducastelle and D. Spanjaard, J. Phys. (Paris), 41 (1980) 281. F. R. McFeely, S. P. Kowalczyk, L. Ley, R. G. Cavell and D. A. Shirley, Phys. Rev. B, 9 (1974) 5268. P. Pfluger, personal communication.