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Carbon XVV Auger lineshape analysis for alkali-intercalated graphite
Solid State Communications, Vol. 35, pp. 501—503. Pergamon Press Ltd. 1980. Printed in Great Britain. CARBON XVV AUGER LINESHAPE ANALYSIS FOR ALKALI-INTERCALATED GRAPHITE* S.D. Bader Materials Science Division, Argonne National laboratory, Argonne, IL 60439, U.S.A. (Received 20 Februa,y 1980 byA.G. Cl1yroweth) A model calculation of the carbon XVV Auger lineshape for alkali— graphite intercalation compounds is presented and compared to the recent experiments of Oelhafen et al. The results provide only limited support for their proposal that new selection rules restrict the Auger self-convolution. IN A VERY RECENT communication [1] Oelhafen, Pfluger and GUntherodt (OPG) presented Auger electron spectroscopy (AES) and ultraviolet photoelectron spectroscopy (UPS) results for the alkali graphite intercalation compounds C8Cs and C8Rb. They found that
eliminate the possibility, that selection rules of the type described in [1] are in operation. The point of view is taken that the lineshape clearly shows the electron-donor nature of the alkali metal, since carbon
the carbon XVV Auger emission, where X represents a core level and V the valence band, for these compounds exhibits a strikingly narrow feature (~ 2 eV wide) at high kinetic energy due to the alkali addition. Features at high kinetic energy in the XVV Auger spectrum are expected to emanate from the low binding energy region of the valence band. Indeed, OPG observed the expected narrow emission (~ 1 eV wide) just below the Fermi energy EF in their HE I UPS results [1, 2]. OPG identifled the narrow Auger feature as being the selfconvolution of the alkali-related contribution to the valence-band density of states. However, they also emphasized that the alkali-related states were not significantly convoluted with the rest of the valence band. From this they introduced the idea of a restricted self convolution and concluded that the experiments “provide direct proof that very strong matrtx element effects or selection rules. are operating. In the present communication the OPG assertion that the alkali-related states are not significantly convoluted with the rest of the valence band is examined in the light of a simple model calculation of the carbon XVV Auger spectra of these materials. The present approach utilizes existing electronic band structure calculations for graphite [3]. It is found that the unrestricted Auger cross-terms calculated between the alkali-related states and the rest of the valence band agree m energy with important secondary features that were observed in the OPG Auger experiments but were not addressed directly. The present re-examination of the carbon XVV Auger lineshape for alkali graphite intercalation compounds casts doubts, but does not —
. .“
____________
*
Work supported by the U.S. Department of Energy.
XVV AES is a highly localized [4] probe of the carbon partial density of states. Thus, the most important section rule is believed to be due to the extremely localized nature of the Auger process. This view has been presented by Jennison in a series of papers where XVV Auger lineshapes were analyzed for Si [5, 6], Li [6], Cu [7] and Be [8]. To effectively evaluate the Auger lineshape for the intercalation-compound case, it first was necessary to generate a realistic graphitic lineshape to serve as a background case. The occupied density of states of graphite Nc(E) expressed per carbon atom is —
where a and ir refer to the symmetries of the subbands, which contain 3 and 1 electron, respectively. The inset in Fig. I shows N0 and N,~for graphite calculated by Painter and Ellis [3] from an ab initio variational approach, and which appeared interpolated into histogram form in a subsequent review article [9]. The graphitic XVV Auger lineshape was then generated from the self-fold [10, 11] of the transition density function N~,which is N0 appropriately weighted to account for differing Auger matrix elements across the band. It was found that the main features of the experimental graphite Auger spectrum could be generated from N~if ,
~
N0(E,
— —
N0~E)+ a7~N~(E,
where a,~weights the ir-subband with respect to the a-subband, for a value of a~= 3, (see Fig. 1). This weighting can be qualitatively rationalized since: (a) the 7r-subband has approximately one-third the width of the o-subband [see inset in Fig. 1], (b) narrow bands, in general, imply localization, while broad bands imply
501
502
AUGER LINESHAPE ANALYSIS FOR ALKALI-INTERCALATED GRAPHITE
~II _Jl~ ~20
1”
-
-
ENERGY 0 (eV)
Er
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~
~
~\
~HITE
230
>-
cn w
-
/
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14 aT
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I...
.
8A
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ELECTRON ENERGY (eV) /
I
I b
2
(2
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280
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Vol. 35, No. 6
I
(2
-.1
-
e GRAPHITE 0 40
I
I
30
20
•—
10
0
ENERGY WITH RESPECT TO Er (eV)
Fig. 1. The calculated Auger spectrum of graphite is plotted for three values of a~,the ir-subband weighting factor. The prominent shoulder and peak, labelled a and b, respectively, agree with experiment for the a,~= 3 curve. The inset shows the density of states of graphite decomposed into its a and ir contributions, based on the calculations of Painter and Ellis. [3, 9]. delocalization, and (c) Jennison’s guidelines [5—8] suggest that the more localized subbands are enhanced in the XVV Auger spectrum. The main features in the = 3 curve in Fig. 1 that also characterized the experimental data [1, 101 are the shoulder labelled a and the peak labelled b. Also plotted in Fig. 1 are calculated self-folds of N~for other values of a7~,to demonstrate the sensitivity of the resultant lineshape to this parameter. We now proceed to the interesting intercalation. compounds case. A narrow density-of-states feature of Gaussian shape is introduced just above the ir-subband to represent the electronic charge donated to the carbon ~ antibonding ir-subband from the alkali atom A, and to recover the sharp structure observed by~OPGin their AES and UPS studies. The effect of cross terms becomes apparent in the comparison of this case with the “background” case just presented. Figure 2 shows the result [dashed curve] assuming N~,A
=
8[N~,+ (XANA],
where air = 3 again, CiA = 8 if the alkali charge transfer is complete (or CiA = 8/f, if f is the fraction transferred
0 40
I
I
I
30
20
0
0
ENERGY WITH RESPECT TO GRAPHITE E~1eV)
Fig. 2. The calculated Auger spectrum of graphite for ce1~= 3 [bold-line curve] is compared to that calculated for the graphite.intercalation compound prototype C8A [dashed curve]. Also included is a calculation for C8A [fine-line curve] performed under the severe assumption that each alkali atom effectively interacts with only two carbon atoms [see text]. The features a and b in the calculations derive from the density of states of graphite, e derives from the alkali charge donated to carbon, and c and d from cross terms between alkali- and graphiterelated states. These same features are~denotedwith primes in the inset, which shows the experimental results for graphite and C8Cs taken from the work of OPG [1]. Note the presence of weak cross-term features c’ and d’ in the experimental results. from atom A), and NA is an appropriately positioned and normalized Gaussian (FWHM = 0.8 eV). The value of CiA is expected to be a~,since the alkali-derived electronic contribution has lr*.character, and the ir -subband is more localized than the ir-subband because it is antibonding with respect to neighbouring carbons. The inset in Fig. 2 shows the OPG experimental results for graphite and C8Cs taken from [1]. For C8A the calculated features labelled a and b in Fig. 2 are prominent as in Fig. 1, and the alkali-related self-fold feature labelled e is in approximate agreement with experiment (see inset). Note that the calculated cross terms labelled c and d are intense and can now also be identified in the experimental results [1] as the weak features labelled c’ and d’(see Fig. 2 inset). Originally the experimental features c’ and d’ might have been
Vol. 35, No.6
AUGER LINESHAPE ANALYSIS FOR ALKALI-INTERCALATEDGRAPHITE
503
overlooked as possible loss processes; however, now such an identification is hardly compelling. The enhanced prominence of the calculated compared to the exper-
found in charge-density-distribution calculations [13] and recent angle-resolved photoemission studies [14] for C6Li. However, only limited support was found in
imental cross terms lends support to the OPG observation that the cross terms are restricted in the selfconvolution, In an attempt to improve agreement between experiment and calculation, without invoking new selection rules that restrict the self-convolution, an additional type of constraint was imposed on the calculation. Considering that crystallographically inequivalent carbons may also differ in their excess charge accepted from the A-site, the calculated Auger spectrum would consist of the sum of the self-folds of a distribution of transition density functions. The justification for such a distribution follows: The C8A structure (Stage I) consists of one graphitic layer between each A layer, which has one-eighth the C-layer atomic density. Within the graphite layer there are 8 inequivalent carbons per primitive cell [12]. For the
the present work that these materials provide a key to new XVV Auger selection rules that minimize crossterm emission. Calculations that utilize realistic wave functions would be of value to deepen our understanding of the Auger data for these very interesting graphite intercalation compounds.
surface, where the Auger signal is not attenuated by mean free path considerations, the symmetry is reduced with respect to the bulk, and the A-layer is on the average one-half the density of the interior A -layers, due to the cleaving process. The resultant distribution would be difficult to construct rigorously. Empirically, fair agreement with experiment was achieved [see thin-line curve of Fig. 2] under the assumption that each A-atom effectively interacts with only two carbon atoms (and CiA has the reasonable value of 4). Although the assumption seems overly severe quantitatively, the general constraint considered is expected in part to be responsible for the suppression of the cross terms, and, hence, to weaken the need to invoke new selection rules for the XVV Auger process. In conclusion it should be stressed that the presence of the narrow carbon XVV Auger feature for the II~’~ intercalation compounds dramatically attests to the electron-donor character of these additions, as has been
Acknowledgements I benefitted from helpful comments by M.B. Brodsky, D.E. Ellis, AJ. Freeman, D. Koelling and L. Richter. —
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
13. 14.
P. Oelhafen, P. Pfluger & H.-J. Guntherodt, Solid State Commun. 32, 885 (1979). P. Oelhafen, P. Pfluger, E. Hauser & H.-J. Guntherodt, Phyx Rev. Lert. 44, 197 (1980). G.S. Painter & D.E. Ellis,Phys. Rev. Bi, 4747 (1970). J.E. Houston, G. Moore & M.G. Lagally, Solid State Commun. 21, 879 (1977). D.R. Jennison, Phys. Rev. Lett. 40, 807 (1978). D.R. Phys. Rev. D.R. Jennison, Jennison,Phy& Rev. B18, B18, 6865 6996 (1978). (1978). D.R. Jennison, H.H. Madden & D.M. Zehner, Phys. Rev. B (in press). I.L. Spain & D.J. Nagel, Mater. ScL Eng. 31, 183 (1977). G.F. Amelio & EJ. Scheibner, Surf ScL 11, 242 (1968). C.J. Powell,Phys. Rev. Lett. 30, 1179 (1973). G.s. Pa~y,Mater.ScL Eng. 31,99(1977); D.D.L Chung, G. Dresseihaus & M.S. Dresseihaus, Mater. ScL Eng. 31, 107 (1977). N.A.W. Holzwarth & S. Rabu, Mater. ScL Eng. 31, 195 (1977); LA. Girifalco & N.A.W. Holzwarth, Mater. Sci~Eng. 31, 201 (1977). W. Eberhardt, I.T. McGovern, E.W. Plummer & J.E. Fisher,Phys. Rev. Lett. 44,200(1980).
eliminate the possibility, that selection rules of the type described in [1] are in operation. The point of view is taken that the lineshape clearly shows the electron-donor nature of the alkali metal, since carbon
the carbon XVV Auger emission, where X represents a core level and V the valence band, for these compounds exhibits a strikingly narrow feature (~ 2 eV wide) at high kinetic energy due to the alkali addition. Features at high kinetic energy in the XVV Auger spectrum are expected to emanate from the low binding energy region of the valence band. Indeed, OPG observed the expected narrow emission (~ 1 eV wide) just below the Fermi energy EF in their HE I UPS results [1, 2]. OPG identifled the narrow Auger feature as being the selfconvolution of the alkali-related contribution to the valence-band density of states. However, they also emphasized that the alkali-related states were not significantly convoluted with the rest of the valence band. From this they introduced the idea of a restricted self convolution and concluded that the experiments “provide direct proof that very strong matrtx element effects or selection rules. are operating. In the present communication the OPG assertion that the alkali-related states are not significantly convoluted with the rest of the valence band is examined in the light of a simple model calculation of the carbon XVV Auger spectra of these materials. The present approach utilizes existing electronic band structure calculations for graphite [3]. It is found that the unrestricted Auger cross-terms calculated between the alkali-related states and the rest of the valence band agree m energy with important secondary features that were observed in the OPG Auger experiments but were not addressed directly. The present re-examination of the carbon XVV Auger lineshape for alkali graphite intercalation compounds casts doubts, but does not —
. .“
____________
*
Work supported by the U.S. Department of Energy.
XVV AES is a highly localized [4] probe of the carbon partial density of states. Thus, the most important section rule is believed to be due to the extremely localized nature of the Auger process. This view has been presented by Jennison in a series of papers where XVV Auger lineshapes were analyzed for Si [5, 6], Li [6], Cu [7] and Be [8]. To effectively evaluate the Auger lineshape for the intercalation-compound case, it first was necessary to generate a realistic graphitic lineshape to serve as a background case. The occupied density of states of graphite Nc(E) expressed per carbon atom is —
where a and ir refer to the symmetries of the subbands, which contain 3 and 1 electron, respectively. The inset in Fig. I shows N0 and N,~for graphite calculated by Painter and Ellis [3] from an ab initio variational approach, and which appeared interpolated into histogram form in a subsequent review article [9]. The graphitic XVV Auger lineshape was then generated from the self-fold [10, 11] of the transition density function N~,which is N0 appropriately weighted to account for differing Auger matrix elements across the band. It was found that the main features of the experimental graphite Auger spectrum could be generated from N~if ,
~
N0(E,
— —
N0~E)+ a7~N~(E,
where a,~weights the ir-subband with respect to the a-subband, for a value of a~= 3, (see Fig. 1). This weighting can be qualitatively rationalized since: (a) the 7r-subband has approximately one-third the width of the o-subband [see inset in Fig. 1], (b) narrow bands, in general, imply localization, while broad bands imply
501
502
AUGER LINESHAPE ANALYSIS FOR ALKALI-INTERCALATED GRAPHITE
~II _Jl~ ~20
1”
-
-
ENERGY 0 (eV)
Er
__
~
~
~\
~HITE
230
>-
cn w
-
/
I /l
14 aT
~
-.
I...
.
8A
d
ELECTRON ENERGY (eV) /
I
I b
2
(2
C
280
b
I.
Vol. 35, No. 6
I
(2
-.1
-
e GRAPHITE 0 40
I
I
30
20
•—
10
0
ENERGY WITH RESPECT TO Er (eV)
Fig. 1. The calculated Auger spectrum of graphite is plotted for three values of a~,the ir-subband weighting factor. The prominent shoulder and peak, labelled a and b, respectively, agree with experiment for the a,~= 3 curve. The inset shows the density of states of graphite decomposed into its a and ir contributions, based on the calculations of Painter and Ellis. [3, 9]. delocalization, and (c) Jennison’s guidelines [5—8] suggest that the more localized subbands are enhanced in the XVV Auger spectrum. The main features in the = 3 curve in Fig. 1 that also characterized the experimental data [1, 101 are the shoulder labelled a and the peak labelled b. Also plotted in Fig. 1 are calculated self-folds of N~for other values of a7~,to demonstrate the sensitivity of the resultant lineshape to this parameter. We now proceed to the interesting intercalation. compounds case. A narrow density-of-states feature of Gaussian shape is introduced just above the ir-subband to represent the electronic charge donated to the carbon ~ antibonding ir-subband from the alkali atom A, and to recover the sharp structure observed by~OPGin their AES and UPS studies. The effect of cross terms becomes apparent in the comparison of this case with the “background” case just presented. Figure 2 shows the result [dashed curve] assuming N~,A
=
8[N~,+ (XANA],
where air = 3 again, CiA = 8 if the alkali charge transfer is complete (or CiA = 8/f, if f is the fraction transferred
0 40
I
I
I
30
20
0
0
ENERGY WITH RESPECT TO GRAPHITE E~1eV)
Fig. 2. The calculated Auger spectrum of graphite for ce1~= 3 [bold-line curve] is compared to that calculated for the graphite.intercalation compound prototype C8A [dashed curve]. Also included is a calculation for C8A [fine-line curve] performed under the severe assumption that each alkali atom effectively interacts with only two carbon atoms [see text]. The features a and b in the calculations derive from the density of states of graphite, e derives from the alkali charge donated to carbon, and c and d from cross terms between alkali- and graphiterelated states. These same features are~denotedwith primes in the inset, which shows the experimental results for graphite and C8Cs taken from the work of OPG [1]. Note the presence of weak cross-term features c’ and d’ in the experimental results. from atom A), and NA is an appropriately positioned and normalized Gaussian (FWHM = 0.8 eV). The value of CiA is expected to be a~,since the alkali-derived electronic contribution has lr*.character, and the ir -subband is more localized than the ir-subband because it is antibonding with respect to neighbouring carbons. The inset in Fig. 2 shows the OPG experimental results for graphite and C8Cs taken from [1]. For C8A the calculated features labelled a and b in Fig. 2 are prominent as in Fig. 1, and the alkali-related self-fold feature labelled e is in approximate agreement with experiment (see inset). Note that the calculated cross terms labelled c and d are intense and can now also be identified in the experimental results [1] as the weak features labelled c’ and d’(see Fig. 2 inset). Originally the experimental features c’ and d’ might have been
Vol. 35, No.6
AUGER LINESHAPE ANALYSIS FOR ALKALI-INTERCALATEDGRAPHITE
503
overlooked as possible loss processes; however, now such an identification is hardly compelling. The enhanced prominence of the calculated compared to the exper-
found in charge-density-distribution calculations [13] and recent angle-resolved photoemission studies [14] for C6Li. However, only limited support was found in
imental cross terms lends support to the OPG observation that the cross terms are restricted in the selfconvolution, In an attempt to improve agreement between experiment and calculation, without invoking new selection rules that restrict the self-convolution, an additional type of constraint was imposed on the calculation. Considering that crystallographically inequivalent carbons may also differ in their excess charge accepted from the A-site, the calculated Auger spectrum would consist of the sum of the self-folds of a distribution of transition density functions. The justification for such a distribution follows: The C8A structure (Stage I) consists of one graphitic layer between each A layer, which has one-eighth the C-layer atomic density. Within the graphite layer there are 8 inequivalent carbons per primitive cell [12]. For the
the present work that these materials provide a key to new XVV Auger selection rules that minimize crossterm emission. Calculations that utilize realistic wave functions would be of value to deepen our understanding of the Auger data for these very interesting graphite intercalation compounds.
surface, where the Auger signal is not attenuated by mean free path considerations, the symmetry is reduced with respect to the bulk, and the A-layer is on the average one-half the density of the interior A -layers, due to the cleaving process. The resultant distribution would be difficult to construct rigorously. Empirically, fair agreement with experiment was achieved [see thin-line curve of Fig. 2] under the assumption that each A-atom effectively interacts with only two carbon atoms (and CiA has the reasonable value of 4). Although the assumption seems overly severe quantitatively, the general constraint considered is expected in part to be responsible for the suppression of the cross terms, and, hence, to weaken the need to invoke new selection rules for the XVV Auger process. In conclusion it should be stressed that the presence of the narrow carbon XVV Auger feature for the II~’~ intercalation compounds dramatically attests to the electron-donor character of these additions, as has been
Acknowledgements I benefitted from helpful comments by M.B. Brodsky, D.E. Ellis, AJ. Freeman, D. Koelling and L. Richter. —
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
13. 14.
P. Oelhafen, P. Pfluger & H.-J. Guntherodt, Solid State Commun. 32, 885 (1979). P. Oelhafen, P. Pfluger, E. Hauser & H.-J. Guntherodt, Phyx Rev. Lert. 44, 197 (1980). G.S. Painter & D.E. Ellis,Phys. Rev. Bi, 4747 (1970). J.E. Houston, G. Moore & M.G. Lagally, Solid State Commun. 21, 879 (1977). D.R. Jennison, Phys. Rev. Lett. 40, 807 (1978). D.R. Phys. Rev. D.R. Jennison, Jennison,Phy& Rev. B18, B18, 6865 6996 (1978). (1978). D.R. Jennison, H.H. Madden & D.M. Zehner, Phys. Rev. B (in press). I.L. Spain & D.J. Nagel, Mater. ScL Eng. 31, 183 (1977). G.F. Amelio & EJ. Scheibner, Surf ScL 11, 242 (1968). C.J. Powell,Phys. Rev. Lett. 30, 1179 (1973). G.s. Pa~y,Mater.ScL Eng. 31,99(1977); D.D.L Chung, G. Dresseihaus & M.S. Dresseihaus, Mater. ScL Eng. 31, 107 (1977). N.A.W. Holzwarth & S. Rabu, Mater. ScL Eng. 31, 195 (1977); LA. Girifalco & N.A.W. Holzwarth, Mater. Sci~Eng. 31, 201 (1977). W. Eberhardt, I.T. McGovern, E.W. Plummer & J.E. Fisher,Phys. Rev. Lett. 44,200(1980).