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Electronic structure studies of intercalated, hetero and endohedral fullerenes
CarbonVol.36, No. 5-6, pp. 625-631, 1998 0 1998Else&r Science Ltd Printed inGreatBritain. All rightsreserved 0008-6223/98 $19.00+ 0.00
PII: SOOO8-6223(98)00007-4
ELECTRONIC STRUCTURE STUDIES OF INTERCALATED, HETERO AND ENDOHEDRAL FULLERENES J. FINK,* T. PICHLER, M. KNUPFER, M. S. GOLDEN, S. HAFFNER, R. FRIEDLEIN, U. KIRBACH, P. KURAN
and L. DUNSCH
Institut ftir Festkorper- und Werkstofforschung Dresden, Postfach 270016,01171 Dresden, Germany (Received 30 October 1997; accepted in revised form 9 December
1997)
Abstract-Electronic structure studies of undoped, intercalated, endohedral and heterofullerenes using photoemission and electron energy-loss spectroscopy are reviewed. In particular, results are presented from higher fullerenes, alkali metal intercalated fullerenes, from undoped and alkali metal doped C,,N and from pristine and alkali metal intercalated Tm@& 0 1998 Elsevier Science Ltd. All rights reserved. Key Words-A. Fullerene, C. electron energy loss spectroscopy (EELS), D. electronic structure.
1.
INTRODUCTION
In 1985 a third allotrope
of carbon,
alkali metal intercalated fullerenes, of (C,,N), and of the endohedral fullerene Tm@C,, are reported. Recently, the latter two systems have been intercalated by alkali metals and first results will be presented of these systems, in which the charge of the carbon cage is changed in two different ways at once. Part of the authors’ work until 1995 has been already reviewed [ 61.
the fullerenes,
et al. [ 11. Since in the production of these fullerenes using laser evaporation of graphite only microscopic amounts of fullerenes could be produced, these materials were of interest only for cluster and molecular scientists. After the discovery of the carbon-arc process by Krlitschmer et al. [2] in which macroscopic amounts of fullerenes could be produced, the field was then opened up to solid state and material science. It was quite clear that one should try to intercalate the new modification of carbon and indeed the intercalated fullerenes showed metallic and superconducting behaviour [3,4], as did the intercalated graphite compounds. The discovery of superconducting transition temperatures of up to 34 K, however, stimulated an enormous activity in fullerene research. During recent years, macroscopic amounts of endohedral fullerenes have become available which represent a second class of compounds, in which the charge on the fullerene molecule can be changed by counterions encapsulated inside the carbon cage. Recently, the heterofullerene, Cs9N, could be produced in macroscopic quantities [ 51using an organic synthetic route. In these systems, the charge on the carbon cage could be altered by “on-ball” doping. The three classes of fullerene compounds in which the charge on the carbon cage can be changed are sketched in Fig. 1. In order to understand the chemical bonding and the transport properties of these new compounds, it is necessary to understand their electronic structure. High-energy spectroscopic studies have contributed much in this respect. This article reviews electronic structure studies by photoemission (PES) and by electron energy-loss spectroscopy (EELS) of various fullerene compounds in the solid state. In particular, results from undoped fullerenes, recent results of was discovered
by Kroto
2. EXPERIMENTAL Sample preparation Fullerene and endohedral fullerene containing soots were prepared by the Kratschmer-Huffman method. The separation and purification was performed by high-performance liquid chromatography. (C,,N), was prepared using an organic synthetic route [5]. For EELS, 1000 A thick films were prepared by sublimation in ultra-high vacuum onto KBr single crystals. Subsequently, the substrate was dissolved in distilled water and the free standing films were mounted on standard electron microscope grids. For PES, thin films with a thickness < 500 A were sublimed onto freshly evaporated Cu or Au films. Alkali metal doping was performed in situ using commercial SAES getter sources. During the doping process the sample was kept at temperatures of ca 100°C. Post-annealing was performed at higher temperatures. 2.1
2.2 Spectroscopy The EELS in transmission measurements were performed using a 170 keV spectrometer described elsewhere [ 71. X-ray induced PES (XPS) was carried out using a commercial spectrometer using monochromatic Al KG(radiation (1486.6 eV). The ultraviolet PES (UPS) was performed using a commercial spectrometer with a noble gas discharge lamp providing radiation at energies of 21.22 and 16.8 eV for operation with He and Ne, respectively.
*Corresponding author. 625
J. FINKPI ul.
626
(c)
(b)
(4
Fig. I. Sketch of the three ways to change the charge on the carbon cage of fullerenes: (a) intercalated compounds (e.g. K,C,,); (b) heterofullerenes (e.g. Cs9N); and (c) endohedral fullerenes (e.g. La@&,). the degeneracy is lifted for 12 3. However, there still remains a rather high degeneracy of the molecular orbitals since the CbOmolecule is that molecule having the highest symmetry among all known molecules. The highest occupied molecular orbital (HOMO) is fivefold degenerate and has h, symmetry and an angular momentum 1=5. The lowest unoccupied molecular orbital (LUMO) has the same angular momentum and t, symmetry. Upon forming a solid, there is a small overlap of the n-orbitals sticking out of the surface of the molecules. The broadening of the individual molecular states into bands is, however, considerably smaller than the energetic spacing between the different molecular orbital levels. This is illustrated in Fig. 2(b) for the HOMO and the LUMO of C,, which, according to bandstructure calculations in the local density approximation ( LDA), develops for fee C,e solid [ 81into five valence bands and three conduction bands, respectively. The width of these bands is ca 0.5 eV which is considerably smaller than the optical bandgap of 1.8 eV. This
3. THEORETICAL PREDICTIONS OF THE FULLERENE AND FULLERIDE ELECTRONIC STRUCTURE
The valence electrons of the fullerenes are mainly in the sp2 configuration as in graphite. Due to the curvature of the fullerene molecules there is an admixture of sp3 hybrids. There are strong cr bonds between the C atoms, which are mainly responsible for the stability of the cage. Perpendicular to the surface of the cage are the C2p, orbitals, which in conjugated C systems accommodate the so-called x electrons which form the weak n-bonds. It is these less strongly bond z-electrons which are responsible for the lowenergy excitations and for the electronic transport properties in fullerene solids. In Fig. 2(a) the molecular orbital scheme for IIelectrons of a C,, molecule is shown, as derived from a tight-binding calculation. Because of the almost spherical potential of the C cage, the level scheme can be classified in terms of the angular momentum. Due to the truncated icosahedral structure, part of
Molecule
I
___ _-_ _ 6
EleW
-me_
____
6
Solid state
---
_
/
5
_-_ - __
N(EI -
Fig. 2. (a) Schematic diagram of the C,, z molecular orbital energy scheme. (b) The bandstructure of the HOMO- and LUMOderived bands of solid C,,. (c) The DOS of the HOMO- and LUMO-derived bands of solid Cc,, (from LDA bandstructure calculations).
Intercalated. hetero and endohedral fullerenes indicates that solid state effects only slightly distort the molecular electronic structure of the fullerenes. This picture also does not change when going to quasiparticle bandstructure calculations. This is necessary to compare theoretical results with excitation spectra. In these bandstructure calculations (using the GW approximation) the quasiparticle gap is predicted to be 2.15 eV with bandwidths of 0.9 and 0.7 eV for the HOMO and the LUMO derived bands, respectively [ 91. In LDA bandstructure calculations, exchange and correlation effects are taken into account in a freeelectron model, which starts with a homogeneous charge distribution. On the other hand, the charge in solid C6,, is mainly concentrated on the carbon cage and is therefore quite inhomogeneous. The localization of the charge is analogous to that in solids having partially filled 3d and 4f levels. In many of these systems and in solid C6e the bandwidth, W, is smaller than the on-site Coulomb repulsion of two electrons on a molecule, U. U between two holes on the same C, molecule has been determined from a comparison of C KVV Auger spectra with valence band PES spectra [lO,ll]. Values of U have been found to be N 1.5 eV which are considerably larger than the bandwidth W=O.5-0.6 eV derived from LDA bandstructure calculations. This raises the question as to whether solid fullerenes can be adequately described in models based upon independent electrons. A further point which questions the applicability of LDA bandstructure calculations for solid Cso is the orientational disorder of the Cso molecules. This orientational disorder is observed in pure C,, as a result of molecular rotation and is also present in intercalated CeOcompounds. Calculations of orientationally disordered K&, indicate that despite the disorder the states in the centre of the conduction band (near Er) remain delocalized and only states at the bottom and at the top of the conduction band are localized due to disorder [ 121. In the intercalated compounds, alkali metal atoms are placed on interstitial sites and they donate their outermost electrons to the fullerenes. This is possible because of the high electron affinity, EA, of solid fullerenes (for solid C6,,, EA is ca 4.5 eV) and the small work function of the alkali metals. Alkali metal &,, fullerides have been prepared with the composition AC,,, A,&,, A$&, A4Cso and A&* In a simple rigid band model, the phases AC,,, A&,, A&, and A&, should have partially filled LUMO-derived conduction bands and should therefore show metallic behaviour. This result is also derived from LDA bandstructure calculations of intercalated compounds [ 13,141. The compound A&, should be an insulator because the three LUMO-derived conduction bands are completely filled. In reality, A&, is a metal, contrary to what is expected from correlation effects, and A.&,,
627
is an insulator, contrary to what is expected from bandstructure calculations. 4. EXPERIMENTAL RESULTS ON SOLID FULLERENRS AND FULLERENE COMPOUNDS
4.1 Undoped fullerenes In Fig. 3(a) PES spectra of various fullerenes are shown, representing in a first approximation the occupied density of states (DOS). For Cso, the two peaks with the lowest binding energy (BE) represent the valence bands derived from the HOMO and from the HOMO-l and HOMO-2, respectively. Below 5 eV BE not only II, but also u orbitals contribute to the PES spectra. The HOMO-derived states for the higher fullerenes are considerably broadened. This can be explained by a lowering of the symmetry of the molecules leading to a lifting of the high degeneracy of the molecular orbitals. For Cad, different isomers with possibly different electronic structure contribute to the measured DOS. That different isomers have quite different electronic structures can be seen from the spectra of two different C,s isomers (2 and 3) which both have Czv symmetry [ 151. In Fig. 3(b) excitations from the C 1s core level into unoccupied conduction band states, measured by EELS are shown. Neglecting excitonic effects, the spectra represent the unoccupied DOS at the C sites. For C&, well resolved peaks are observed once more. Below 290 eV, these features can be assigned to unoccupied x* bands, while above 290 eV o* bands also contribute. The lowest peak at 284.5 eV corresponds to the LUMO-derived lowest group of conduction bands. Again, the features for the higher fullerenes are broadened due to the lower symmetry of the molecules and in some cases due to contributions from different isomers. In Fig. 4, valence band excitations between the x and x* bands, measured by EELS are shown. Again, narrow features are observed for Cm while for the higher fullerenes, all transitions are broadened. The observed gap for C&, is 1.8 eV. For the higher fullerenes, this gap decreases reaching a value of 1.2 eV for Ca4. This is expected, because in the higher
10 8 (a)
6
4
2
hdiwnwgy(eV)
0
282284 21288 290 292 (b)
Enagyo
Fig. 3. (a) PES spectra of various fullerenes. (b) C 1s excitation spectra of various fullerenes, measured by EELS.
628
J. FINK et ul.
0
2
4
6
8 10 12
Energy (eV) Fig. 4. EELS of various
solid fullerenes.
fullerenes more and more hexagons are placed between the 20 pentagons leading to an increasingly graphite-like structure. The reduction of the gap can then be understood from the fact that graphite is a semi-metal. 4.2 lntercaledfidlerene compounds In Fig. 5 typical experimental spectra of A.&,, (A = K) compounds is shown. Figure 5(a) shows PES spectra Fig. 5(b) depicts C Is excitation spectra. In the PES spectra of K&,,,, a new peak at low BE is realized. That peak shows a clear Fermi edge as is expected for a metal. The strong broadening of this feature compared to half of the bandwidth (0.3 eV) derived from LDA bandstructure calculations has been explained by the emission of phonons (related to molecular vibrations) and plasmons satellites [ 161 or by the presence of satellites due to correlation PES spectrum shows no effects [ 171. The K,C,, Fermi edge, contrary to what is expected from LDA bandstructure calculations. The spectrum for K,C,,
I
Z
a
284 543210 (a) Binding energy (eV) (b)
EELSCls
286
288
(
290
Energy (ev)
Fig. 5. Spectroscopic data for K,C,,. (a) PES spectra, related to the occupied DOS. (b) C Is excitation spectra, measured by EELS. The latter are related to the unoccupied DOS.
shows a completely filled LUMO-derived conduction band in agreement with the fact that these three bands can be filled with six electrons. In Fig. 5(b) typical C 1s excitation spectra for KxC6,, are shown. For K,C,,, the peak with the lowest excitation energy is reduced by a factor of two when compared with C,,, consistent with the filling of the LUMO-derived bands by three electrons. In K,C,, this peak is further reduced while due to the complete filling of the bands, it has completely disappeared for K,C,,. To understand the metallic behaviour of the A&,, compounds and the insulating behaviour of the A&, systems, a detailed study of the energy gap of the A&, compounds for various alkali metals was performed [ 181. In Fig. 6 (a) the optical conductivity of several A4C6,, compounds is shown. The data were derived from EELS spectra using the Kramers-Kronig relation. Data of Na&& are also included. In the latter, eight electrons are transferred to the C& so that the LUMO+ 1 derived bands contain two electrons [ 191 which is equivalent to four holes. One can see that the gap is strongly dependent on both the lattice constant and the crystal symmetry. In Fig. 5(b) the gap, A, is shown as a function of the nearest neighbour distance d for the bet compounds A&,, (A = K, Rb, Cs) and for the fee compounds Na,C,, and Nan&. Recently, it has been pointed out [20] that the gap in a correlated system is not just U-W but transforms in a system with orbital degeneracy N into
where U,, is the bare on-site correlation energy, and iiU is the polarization screening of this quantity. Both the screening and the width depend upon the crystal symmetry and the lattice constants. In addition the prefactor fl depends slightly on the filling of the bands. The calculated dependence of the gap IS shown by solid lines in Fig. 6(b) and agrees well with the experimental data. This is a strong indication that the insulating behaviour of the A&,, compounds can be described in a MotttHubbard picture. The metallic character of the A$,, compounds can then be rationalized by a reduction of the Coulomb energy U by a Jahn-Teller contribution [21]. 4.3 Heterojiillerenes A second way by which the charge on the fullerene cages can be changed is the replacement of a C atom by atoms having a different valency, for example, B or N. As pointed out before, the preparation of (C,,N), molecules has been recently achieved [5]. In a naive picture, one would expect a metallic behaviour of solid Cs,N due to a partial filling of the conduction band with the “additional” electron coming from the N atom. A detailed study of solid (C&N )2 by high-energy spectroscopy was performed [22]. In Fig. 7 the valence band PES and the EELS C 1s and N 1s core excitation spectra of solid (C&N )2 is shown. These experimental data are com-
Intercalated, hetero and endohedral fullerenes
j
i
i
629
(4 Fig. 6. (a) The optical conductivity, u, of A&, (A=Na, K, Rb and Cs) and Na,,C,, as derived from the measured loss functions. (b) Energy gap, A, of AJ& and Na,,C, compounds as a function of the nearest neighbour distance d. The solid lines show the expected behaviour for fee (lower line) and bet phases (upper line) within a simple Mott-Hubbard model.
L 10
I
I
8
6
Binding
-
,
I
4
2
energy WI
.
I
0 282
284
.
I
286
.
I
288
.
I
290
.
292
Energy W
Fig. 7. Valence band photoemission spectra (0) and C 1s core level excitation spectra (0) of solid (C,,N),. Also shown is the N 1s excitation spectrum (e) of the heterofullerene. The experimental data are compared with the calculated partial DOS at the N sites and with the total DOS [21]. pared to calculations of the partial DOS at the N-sites and the calculated total DOS. The overall shape of the PES spectra and the C 1s excitation spectra of the heterofullerene is very similar to that of C,,. In (C59N)Z there is only some extra broadening of the spectral features, which can be explained by a lowering of the symmetry due to the dimer formation and by the substitution of one of the C atoms adjacent to the C-C intermolecular bond by an N atom. The PES spectrum of (&N)* has at the lowest BE a shoulder near ca 1.9 eV, which, upon consideration of the theoretical partial DOS at the N-atoms, can be related to the extra electron which actually maintains a high degree of N-character. Calculation of the spatial distribution of the charge density of this new HOMO yields a strong concentration near the N-atoms and along the intermolecular bond of the dimer. The lack of a strong feature in the N 1s excitation spectrum at energies corresponding to the LUMO of Ceo in the C Is excitation spectrum also lends weight to the
arguments put forward above in favour of the localization of the extra electron. In conclusion, the extra electron in the heterofullerene does not occupy the Cso LUMO to form a metallic state. Rather, the extra electrons occupy a new HOMO at the bottom of the gap, which is formed due to the additional core potential at the N atom and the dimerization. Recently, the electronic structure of intercalated C59N was investigated. At present, K&&N is the only heterofullerene salt to have been prepared in a phase pure form and to have been fully structurally characterized [23]. From this it is known that K&&N is isostructural with bee K6&, and that the heterofullerene molecules are present as monomers. The PES spectra of K&N (not shown) indicate at least one intermediate phase between the end members x = 0 and x = 6. The valence band PES spectra and the C 1s core excitation spectra for x = 6 are very similar to those of K&,. At present, therefore, it is not clear where the extra electron from the N atom in K6C&, N is located, as from the measurements no filling of the (LUMO + 1)-derived bands could be detected. It remains a puzzle why K&,N is not a metal. 4.4 Endohedralfullerenes Since the first extraction in 1991 [24], a large number of different endohedral fullerenes have been extracted, predominantly in which SC, Y or rare earth ions are encapsulated. The electronic structure of these endohedral monometallofullerenes was formally described as M3+ @Ci;, which is consistent with ESR experiments [25] and theoretical calculations [26,27]. However, there are only a few experimental studies of the electronic structure of endohedral fullerenes. For example, from the La 3d core level XPS spectrum of La@&, a formal charge state La3+ @Ci; was found [28]. Here UPS and XPS measurements on the C3, isomer of Tm@Cs, are reported [29]. The current investigations of the other two stable isomers, resulting from the separa-
630
3. FINK et al.
AE,&,, AE = alkaline-earth metals) have been discovered up to now, although there are now three different ways to change the charge on the fullerene cage (intercalated, hetero and endohedral fullerenes). It remains remarkable that up to now no metallic compound from higher fullerenes (C,,, C,,, C,,, C,,) could be detected. Acknowledgements~The authors acknowledge the BMBF for financial support under the Contract No. 13N6676/7. T.P. thanks the European Union for funding under the “Training and Mobility of Researchers” programme. S.H. acknowledges the support of the DFG (Graduiertenkolleg TU-Dresden).
REFERENCES
15
10
5
0
Binding energy (eV) Fig. 8. XPS valence band spectra Tm@C,, and of Tm metal, including
of the C,, 4f multiplets
isomer of calculated
using an intermediate coupling scheme [29]. 4.
will be reported in the future. In Fig. 8 valence band XPS spectra of the C,., isomer of Tm@Cs, and Tm metal both measured using a monochromatic Al K, radiation ( 1486.6 eV ) are shown. At this high photon energy, the relative photoionization cross-section of the Tm 4f states is much greater than that of the C 2p and 2s states. Therefore, the spectra are dominated by the 4f multiplets which can be calculated using the fractional parentage scheme [30]. As shown in Fig. 8 the observed 4f multiplets for Tm metal correspond to a 4f ‘*-+4f l1 transition while those of Tm@C,, corresponds to a 4f 13+4f’* transition. This clearly indicates that in the ground state Tm metal has a 4f’* configuration and is therefore trivalent, while Tm@C,, has a 4f13 configuration and is therefore divalent. Recently, the first experiments on Cs intercalated Tm@Cs2 were performed. The UPS spectra of Cs, (Tm@C,,) show a filling of the LUMO and the LUMO+ 1 derived bands with increasing x. A metallic phase could not be detected so far. tion
process,
5. CONCLUSION During the last 6 years there has been considerable progress in the understanding of the electronic structure of fullerenes and fullerene compounds. In all these systems the electronic structure is dominated by that of the molecules themselves. The weak intermolecular overlap and the strong localization of the charge on the fullerene cages make correlation effects rather important. This may be the reason why only so few metallic fullerene compounds (A,&, and
.5 6.
I. 8. 9. IO.
II. 12. 13. 14. 15.
16.
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18. 19.
20. 21.
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PII: SOOO8-6223(98)00007-4
ELECTRONIC STRUCTURE STUDIES OF INTERCALATED, HETERO AND ENDOHEDRAL FULLERENES J. FINK,* T. PICHLER, M. KNUPFER, M. S. GOLDEN, S. HAFFNER, R. FRIEDLEIN, U. KIRBACH, P. KURAN
and L. DUNSCH
Institut ftir Festkorper- und Werkstofforschung Dresden, Postfach 270016,01171 Dresden, Germany (Received 30 October 1997; accepted in revised form 9 December
1997)
Abstract-Electronic structure studies of undoped, intercalated, endohedral and heterofullerenes using photoemission and electron energy-loss spectroscopy are reviewed. In particular, results are presented from higher fullerenes, alkali metal intercalated fullerenes, from undoped and alkali metal doped C,,N and from pristine and alkali metal intercalated Tm@& 0 1998 Elsevier Science Ltd. All rights reserved. Key Words-A. Fullerene, C. electron energy loss spectroscopy (EELS), D. electronic structure.
1.
INTRODUCTION
In 1985 a third allotrope
of carbon,
alkali metal intercalated fullerenes, of (C,,N), and of the endohedral fullerene Tm@C,, are reported. Recently, the latter two systems have been intercalated by alkali metals and first results will be presented of these systems, in which the charge of the carbon cage is changed in two different ways at once. Part of the authors’ work until 1995 has been already reviewed [ 61.
the fullerenes,
et al. [ 11. Since in the production of these fullerenes using laser evaporation of graphite only microscopic amounts of fullerenes could be produced, these materials were of interest only for cluster and molecular scientists. After the discovery of the carbon-arc process by Krlitschmer et al. [2] in which macroscopic amounts of fullerenes could be produced, the field was then opened up to solid state and material science. It was quite clear that one should try to intercalate the new modification of carbon and indeed the intercalated fullerenes showed metallic and superconducting behaviour [3,4], as did the intercalated graphite compounds. The discovery of superconducting transition temperatures of up to 34 K, however, stimulated an enormous activity in fullerene research. During recent years, macroscopic amounts of endohedral fullerenes have become available which represent a second class of compounds, in which the charge on the fullerene molecule can be changed by counterions encapsulated inside the carbon cage. Recently, the heterofullerene, Cs9N, could be produced in macroscopic quantities [ 51using an organic synthetic route. In these systems, the charge on the carbon cage could be altered by “on-ball” doping. The three classes of fullerene compounds in which the charge on the carbon cage can be changed are sketched in Fig. 1. In order to understand the chemical bonding and the transport properties of these new compounds, it is necessary to understand their electronic structure. High-energy spectroscopic studies have contributed much in this respect. This article reviews electronic structure studies by photoemission (PES) and by electron energy-loss spectroscopy (EELS) of various fullerene compounds in the solid state. In particular, results from undoped fullerenes, recent results of was discovered
by Kroto
2. EXPERIMENTAL Sample preparation Fullerene and endohedral fullerene containing soots were prepared by the Kratschmer-Huffman method. The separation and purification was performed by high-performance liquid chromatography. (C,,N), was prepared using an organic synthetic route [5]. For EELS, 1000 A thick films were prepared by sublimation in ultra-high vacuum onto KBr single crystals. Subsequently, the substrate was dissolved in distilled water and the free standing films were mounted on standard electron microscope grids. For PES, thin films with a thickness < 500 A were sublimed onto freshly evaporated Cu or Au films. Alkali metal doping was performed in situ using commercial SAES getter sources. During the doping process the sample was kept at temperatures of ca 100°C. Post-annealing was performed at higher temperatures. 2.1
2.2 Spectroscopy The EELS in transmission measurements were performed using a 170 keV spectrometer described elsewhere [ 71. X-ray induced PES (XPS) was carried out using a commercial spectrometer using monochromatic Al KG(radiation (1486.6 eV). The ultraviolet PES (UPS) was performed using a commercial spectrometer with a noble gas discharge lamp providing radiation at energies of 21.22 and 16.8 eV for operation with He and Ne, respectively.
*Corresponding author. 625
J. FINKPI ul.
626
(c)
(b)
(4
Fig. I. Sketch of the three ways to change the charge on the carbon cage of fullerenes: (a) intercalated compounds (e.g. K,C,,); (b) heterofullerenes (e.g. Cs9N); and (c) endohedral fullerenes (e.g. La@&,). the degeneracy is lifted for 12 3. However, there still remains a rather high degeneracy of the molecular orbitals since the CbOmolecule is that molecule having the highest symmetry among all known molecules. The highest occupied molecular orbital (HOMO) is fivefold degenerate and has h, symmetry and an angular momentum 1=5. The lowest unoccupied molecular orbital (LUMO) has the same angular momentum and t, symmetry. Upon forming a solid, there is a small overlap of the n-orbitals sticking out of the surface of the molecules. The broadening of the individual molecular states into bands is, however, considerably smaller than the energetic spacing between the different molecular orbital levels. This is illustrated in Fig. 2(b) for the HOMO and the LUMO of C,, which, according to bandstructure calculations in the local density approximation ( LDA), develops for fee C,e solid [ 81into five valence bands and three conduction bands, respectively. The width of these bands is ca 0.5 eV which is considerably smaller than the optical bandgap of 1.8 eV. This
3. THEORETICAL PREDICTIONS OF THE FULLERENE AND FULLERIDE ELECTRONIC STRUCTURE
The valence electrons of the fullerenes are mainly in the sp2 configuration as in graphite. Due to the curvature of the fullerene molecules there is an admixture of sp3 hybrids. There are strong cr bonds between the C atoms, which are mainly responsible for the stability of the cage. Perpendicular to the surface of the cage are the C2p, orbitals, which in conjugated C systems accommodate the so-called x electrons which form the weak n-bonds. It is these less strongly bond z-electrons which are responsible for the lowenergy excitations and for the electronic transport properties in fullerene solids. In Fig. 2(a) the molecular orbital scheme for IIelectrons of a C,, molecule is shown, as derived from a tight-binding calculation. Because of the almost spherical potential of the C cage, the level scheme can be classified in terms of the angular momentum. Due to the truncated icosahedral structure, part of
Molecule
I
___ _-_ _ 6
EleW
-me_
____
6
Solid state
---
_
/
5
_-_ - __
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Fig. 2. (a) Schematic diagram of the C,, z molecular orbital energy scheme. (b) The bandstructure of the HOMO- and LUMOderived bands of solid C,,. (c) The DOS of the HOMO- and LUMO-derived bands of solid Cc,, (from LDA bandstructure calculations).
Intercalated. hetero and endohedral fullerenes indicates that solid state effects only slightly distort the molecular electronic structure of the fullerenes. This picture also does not change when going to quasiparticle bandstructure calculations. This is necessary to compare theoretical results with excitation spectra. In these bandstructure calculations (using the GW approximation) the quasiparticle gap is predicted to be 2.15 eV with bandwidths of 0.9 and 0.7 eV for the HOMO and the LUMO derived bands, respectively [ 91. In LDA bandstructure calculations, exchange and correlation effects are taken into account in a freeelectron model, which starts with a homogeneous charge distribution. On the other hand, the charge in solid C6,, is mainly concentrated on the carbon cage and is therefore quite inhomogeneous. The localization of the charge is analogous to that in solids having partially filled 3d and 4f levels. In many of these systems and in solid C6e the bandwidth, W, is smaller than the on-site Coulomb repulsion of two electrons on a molecule, U. U between two holes on the same C, molecule has been determined from a comparison of C KVV Auger spectra with valence band PES spectra [lO,ll]. Values of U have been found to be N 1.5 eV which are considerably larger than the bandwidth W=O.5-0.6 eV derived from LDA bandstructure calculations. This raises the question as to whether solid fullerenes can be adequately described in models based upon independent electrons. A further point which questions the applicability of LDA bandstructure calculations for solid Cso is the orientational disorder of the Cso molecules. This orientational disorder is observed in pure C,, as a result of molecular rotation and is also present in intercalated CeOcompounds. Calculations of orientationally disordered K&, indicate that despite the disorder the states in the centre of the conduction band (near Er) remain delocalized and only states at the bottom and at the top of the conduction band are localized due to disorder [ 121. In the intercalated compounds, alkali metal atoms are placed on interstitial sites and they donate their outermost electrons to the fullerenes. This is possible because of the high electron affinity, EA, of solid fullerenes (for solid C6,,, EA is ca 4.5 eV) and the small work function of the alkali metals. Alkali metal &,, fullerides have been prepared with the composition AC,,, A,&,, A$&, A4Cso and A&* In a simple rigid band model, the phases AC,,, A&,, A&, and A&, should have partially filled LUMO-derived conduction bands and should therefore show metallic behaviour. This result is also derived from LDA bandstructure calculations of intercalated compounds [ 13,141. The compound A&, should be an insulator because the three LUMO-derived conduction bands are completely filled. In reality, A&, is a metal, contrary to what is expected from correlation effects, and A.&,,
627
is an insulator, contrary to what is expected from bandstructure calculations. 4. EXPERIMENTAL RESULTS ON SOLID FULLERENRS AND FULLERENE COMPOUNDS
4.1 Undoped fullerenes In Fig. 3(a) PES spectra of various fullerenes are shown, representing in a first approximation the occupied density of states (DOS). For Cso, the two peaks with the lowest binding energy (BE) represent the valence bands derived from the HOMO and from the HOMO-l and HOMO-2, respectively. Below 5 eV BE not only II, but also u orbitals contribute to the PES spectra. The HOMO-derived states for the higher fullerenes are considerably broadened. This can be explained by a lowering of the symmetry of the molecules leading to a lifting of the high degeneracy of the molecular orbitals. For Cad, different isomers with possibly different electronic structure contribute to the measured DOS. That different isomers have quite different electronic structures can be seen from the spectra of two different C,s isomers (2 and 3) which both have Czv symmetry [ 151. In Fig. 3(b) excitations from the C 1s core level into unoccupied conduction band states, measured by EELS are shown. Neglecting excitonic effects, the spectra represent the unoccupied DOS at the C sites. For C&, well resolved peaks are observed once more. Below 290 eV, these features can be assigned to unoccupied x* bands, while above 290 eV o* bands also contribute. The lowest peak at 284.5 eV corresponds to the LUMO-derived lowest group of conduction bands. Again, the features for the higher fullerenes are broadened due to the lower symmetry of the molecules and in some cases due to contributions from different isomers. In Fig. 4, valence band excitations between the x and x* bands, measured by EELS are shown. Again, narrow features are observed for Cm while for the higher fullerenes, all transitions are broadened. The observed gap for C&, is 1.8 eV. For the higher fullerenes, this gap decreases reaching a value of 1.2 eV for Ca4. This is expected, because in the higher
10 8 (a)
6
4
2
hdiwnwgy(eV)
0
282284 21288 290 292 (b)
Enagyo
Fig. 3. (a) PES spectra of various fullerenes. (b) C 1s excitation spectra of various fullerenes, measured by EELS.
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0
2
4
6
8 10 12
Energy (eV) Fig. 4. EELS of various
solid fullerenes.
fullerenes more and more hexagons are placed between the 20 pentagons leading to an increasingly graphite-like structure. The reduction of the gap can then be understood from the fact that graphite is a semi-metal. 4.2 lntercaledfidlerene compounds In Fig. 5 typical experimental spectra of A.&,, (A = K) compounds is shown. Figure 5(a) shows PES spectra Fig. 5(b) depicts C Is excitation spectra. In the PES spectra of K&,,,, a new peak at low BE is realized. That peak shows a clear Fermi edge as is expected for a metal. The strong broadening of this feature compared to half of the bandwidth (0.3 eV) derived from LDA bandstructure calculations has been explained by the emission of phonons (related to molecular vibrations) and plasmons satellites [ 161 or by the presence of satellites due to correlation PES spectrum shows no effects [ 171. The K,C,, Fermi edge, contrary to what is expected from LDA bandstructure calculations. The spectrum for K,C,,
I
Z
a
284 543210 (a) Binding energy (eV) (b)
EELSCls
286
288
(
290
Energy (ev)
Fig. 5. Spectroscopic data for K,C,,. (a) PES spectra, related to the occupied DOS. (b) C Is excitation spectra, measured by EELS. The latter are related to the unoccupied DOS.
shows a completely filled LUMO-derived conduction band in agreement with the fact that these three bands can be filled with six electrons. In Fig. 5(b) typical C 1s excitation spectra for KxC6,, are shown. For K,C,,, the peak with the lowest excitation energy is reduced by a factor of two when compared with C,,, consistent with the filling of the LUMO-derived bands by three electrons. In K,C,, this peak is further reduced while due to the complete filling of the bands, it has completely disappeared for K,C,,. To understand the metallic behaviour of the A&,, compounds and the insulating behaviour of the A&, systems, a detailed study of the energy gap of the A&, compounds for various alkali metals was performed [ 181. In Fig. 6 (a) the optical conductivity of several A4C6,, compounds is shown. The data were derived from EELS spectra using the Kramers-Kronig relation. Data of Na&& are also included. In the latter, eight electrons are transferred to the C& so that the LUMO+ 1 derived bands contain two electrons [ 191 which is equivalent to four holes. One can see that the gap is strongly dependent on both the lattice constant and the crystal symmetry. In Fig. 5(b) the gap, A, is shown as a function of the nearest neighbour distance d for the bet compounds A&,, (A = K, Rb, Cs) and for the fee compounds Na,C,, and Nan&. Recently, it has been pointed out [20] that the gap in a correlated system is not just U-W but transforms in a system with orbital degeneracy N into
where U,, is the bare on-site correlation energy, and iiU is the polarization screening of this quantity. Both the screening and the width depend upon the crystal symmetry and the lattice constants. In addition the prefactor fl depends slightly on the filling of the bands. The calculated dependence of the gap IS shown by solid lines in Fig. 6(b) and agrees well with the experimental data. This is a strong indication that the insulating behaviour of the A&,, compounds can be described in a MotttHubbard picture. The metallic character of the A$,, compounds can then be rationalized by a reduction of the Coulomb energy U by a Jahn-Teller contribution [21]. 4.3 Heterojiillerenes A second way by which the charge on the fullerene cages can be changed is the replacement of a C atom by atoms having a different valency, for example, B or N. As pointed out before, the preparation of (C,,N), molecules has been recently achieved [5]. In a naive picture, one would expect a metallic behaviour of solid Cs,N due to a partial filling of the conduction band with the “additional” electron coming from the N atom. A detailed study of solid (C&N )2 by high-energy spectroscopy was performed [22]. In Fig. 7 the valence band PES and the EELS C 1s and N 1s core excitation spectra of solid (C&N )2 is shown. These experimental data are com-
Intercalated, hetero and endohedral fullerenes
j
i
i
629
(4 Fig. 6. (a) The optical conductivity, u, of A&, (A=Na, K, Rb and Cs) and Na,,C,, as derived from the measured loss functions. (b) Energy gap, A, of AJ& and Na,,C, compounds as a function of the nearest neighbour distance d. The solid lines show the expected behaviour for fee (lower line) and bet phases (upper line) within a simple Mott-Hubbard model.
L 10
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6
Binding
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,
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energy WI
.
I
0 282
284
.
I
286
.
I
288
.
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290
.
292
Energy W
Fig. 7. Valence band photoemission spectra (0) and C 1s core level excitation spectra (0) of solid (C,,N),. Also shown is the N 1s excitation spectrum (e) of the heterofullerene. The experimental data are compared with the calculated partial DOS at the N sites and with the total DOS [21]. pared to calculations of the partial DOS at the N-sites and the calculated total DOS. The overall shape of the PES spectra and the C 1s excitation spectra of the heterofullerene is very similar to that of C,,. In (C59N)Z there is only some extra broadening of the spectral features, which can be explained by a lowering of the symmetry due to the dimer formation and by the substitution of one of the C atoms adjacent to the C-C intermolecular bond by an N atom. The PES spectrum of (&N)* has at the lowest BE a shoulder near ca 1.9 eV, which, upon consideration of the theoretical partial DOS at the N-atoms, can be related to the extra electron which actually maintains a high degree of N-character. Calculation of the spatial distribution of the charge density of this new HOMO yields a strong concentration near the N-atoms and along the intermolecular bond of the dimer. The lack of a strong feature in the N 1s excitation spectrum at energies corresponding to the LUMO of Ceo in the C Is excitation spectrum also lends weight to the
arguments put forward above in favour of the localization of the extra electron. In conclusion, the extra electron in the heterofullerene does not occupy the Cso LUMO to form a metallic state. Rather, the extra electrons occupy a new HOMO at the bottom of the gap, which is formed due to the additional core potential at the N atom and the dimerization. Recently, the electronic structure of intercalated C59N was investigated. At present, K&&N is the only heterofullerene salt to have been prepared in a phase pure form and to have been fully structurally characterized [23]. From this it is known that K&&N is isostructural with bee K6&, and that the heterofullerene molecules are present as monomers. The PES spectra of K&N (not shown) indicate at least one intermediate phase between the end members x = 0 and x = 6. The valence band PES spectra and the C 1s core excitation spectra for x = 6 are very similar to those of K&,. At present, therefore, it is not clear where the extra electron from the N atom in K6C&, N is located, as from the measurements no filling of the (LUMO + 1)-derived bands could be detected. It remains a puzzle why K&,N is not a metal. 4.4 Endohedralfullerenes Since the first extraction in 1991 [24], a large number of different endohedral fullerenes have been extracted, predominantly in which SC, Y or rare earth ions are encapsulated. The electronic structure of these endohedral monometallofullerenes was formally described as M3+ @Ci;, which is consistent with ESR experiments [25] and theoretical calculations [26,27]. However, there are only a few experimental studies of the electronic structure of endohedral fullerenes. For example, from the La 3d core level XPS spectrum of La@&, a formal charge state La3+ @Ci; was found [28]. Here UPS and XPS measurements on the C3, isomer of Tm@Cs, are reported [29]. The current investigations of the other two stable isomers, resulting from the separa-
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AE,&,, AE = alkaline-earth metals) have been discovered up to now, although there are now three different ways to change the charge on the fullerene cage (intercalated, hetero and endohedral fullerenes). It remains remarkable that up to now no metallic compound from higher fullerenes (C,,, C,,, C,,, C,,) could be detected. Acknowledgements~The authors acknowledge the BMBF for financial support under the Contract No. 13N6676/7. T.P. thanks the European Union for funding under the “Training and Mobility of Researchers” programme. S.H. acknowledges the support of the DFG (Graduiertenkolleg TU-Dresden).
REFERENCES
15
10
5
0
Binding energy (eV) Fig. 8. XPS valence band spectra Tm@C,, and of Tm metal, including
of the C,, 4f multiplets
isomer of calculated
using an intermediate coupling scheme [29]. 4.
will be reported in the future. In Fig. 8 valence band XPS spectra of the C,., isomer of Tm@Cs, and Tm metal both measured using a monochromatic Al K, radiation ( 1486.6 eV ) are shown. At this high photon energy, the relative photoionization cross-section of the Tm 4f states is much greater than that of the C 2p and 2s states. Therefore, the spectra are dominated by the 4f multiplets which can be calculated using the fractional parentage scheme [30]. As shown in Fig. 8 the observed 4f multiplets for Tm metal correspond to a 4f ‘*-+4f l1 transition while those of Tm@C,, corresponds to a 4f 13+4f’* transition. This clearly indicates that in the ground state Tm metal has a 4f’* configuration and is therefore trivalent, while Tm@C,, has a 4f13 configuration and is therefore divalent. Recently, the first experiments on Cs intercalated Tm@Cs2 were performed. The UPS spectra of Cs, (Tm@C,,) show a filling of the LUMO and the LUMO+ 1 derived bands with increasing x. A metallic phase could not be detected so far. tion
process,
5. CONCLUSION During the last 6 years there has been considerable progress in the understanding of the electronic structure of fullerenes and fullerene compounds. In all these systems the electronic structure is dominated by that of the molecules themselves. The weak intermolecular overlap and the strong localization of the charge on the fullerene cages make correlation effects rather important. This may be the reason why only so few metallic fullerene compounds (A,&, and
.5 6.
I. 8. 9. IO.
II. 12. 13. 14. 15.
16.
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18. 19.
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