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Optical properties of solid C60
S ,Jn IHI III m Tf LLS ELSEVIER
Synthetic Metals 83 (1996) 213-219
Optical properties of solid C6o M. M u c c i n i * Istituto di Spettroscopia Molecolare del CNR, via Gobetti 101, 1-40129 Bologna, Italy
Abstract The opticai properties of materials are strongly related to the nature of the photoexcitations in the solid. FuIlerene C6o in the solid state is a typical molecular material in which the molecules are weakly held together by van der Waals forces and the electronic excitations are very close in energy and nature to those of the free molecule. The lowest electronic states in solid C6o are dipole forbidden and can be described as tight bound (Frenkel) excitons. Optical emission of C6o single crystals can be explained in terms of photoluminescence sub-spectra built on vibronically allowed false origins. Further to these neutral excitations which determine the optical gap there are charged excitations corresponding to the promotion of electrons from ball to ball and from ball to the free electron continuum. We observe intermolecuIar chargetransfer excitons by measuring the electroabsorption of thin films at liquid helium temperature. The energy necessary to generate directly the electron-hole (e-h) pairs is set at least 0.6 eV higher than the optical gap. Keywords: Fullerene; Optical properties
1. Introduction Since fullerene C6o has become available in macroscopic quantities there has been an ongoing experimental and theoretical effort to understand its electronic and optical properties. The electronic energetics of molecular C6o is determined by the 60 electrons on p orbitals, one on each carbon atom, while the cage is formed by the overlap of sp 2 hybridized orbitals. Each p orbital makes a small angle with adjacent orbitals (23.2°). The overlap between orbitals allows therefore the formation of an extended n'r electronic system. Using the one-electron description of the electronic structure, according to the Htickel molecular orbital approach, one gets a closed shell system with a considerable gap between HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) orbitals. Furthermore, the high symmetry of the molecule gives rise to a large degeneracy of the molecular orbitals. Electronic promotion from HOMO (hu) to LUMO (tlu) is forbidden for electric dipole operator and, therefore, it is forbidden for linear optical absorption, while promotions from HOMO - I (gg, hg) to LUMO and HOMO to LUMO + 1 (txg) are allowed. The theoretical investigation of a more rigorous treatment of the electronic structure should include Coulomb interactions. In fact, in "rr conjugated molecules, it has been recog* Corresponding author. Fax: +39 51 639 8539. 0379-6779/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved P//S0379-6779 (96)04472-4
nized long ago [ 1] that inclusion of e-e correlation is essential to reproduce the low energy excitations. In the multielectron approach, the electronic states are classified according to the molecular point group which, in the case of the hycosahedral C6o molecule, is Ih. The molecular nature of solid C6o is well established by the many experimental results of the last few years. One of the most convincing evidence is given by the electronic absorption spectrum. The spectrum of a thin film was reported for the first time by Kr~itschmer et al. [2]. The absorption spectrum consists of a very weak and broad system extending from 1.9 to 2.7 eV (650-450 nm) and of a series of sharp bands at 3.65 eV (339 nm), 4.70 eV (264 nm) and 5.74 eV (216 nm). The solution spectrum [3] is very similar to the solid spectrum [2,4,5] and has been analysed in terms of Herzberg-Teller vibronic coupling (see Section 2). The similarity between the spectra of isolated molecules and the solid implies that the intermolecular interactions are weak, due to van der Waals forces and, therefore, the solid is a typical molecular crystal. B and-structure calculation in the local density approximation (LDA) gives a value of about 1 eV for the optical gap [6], significantly different from that obtained by photoemission spectroscopy (PES) and inverse photoemission spectroscopy (IPES) which results in a factor of two larger. The many-electron effects are taken into account in the quasi-particle approach, leading to a gap and to HOMO and LUMO bandwidths in agreement with the photoemission data.
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M. Muccini /Synthetic Metals 83 (1996) 213-219
Localized electronic excitations and weak intermolecular interactions constitute the main ingredients for the description of the low energy electronic excitations in molecular solids. Major contributions to this field have been given by Davydov [7 ] and Craig and Walmsley [ 8]. Intermolecular interaction in the solid causes a shift of energy in the electronic levels of the free molecule and a spreading of the levels into bands, whose widths depend on the interaction between translationally non-equivalent molecules [ 7 ]. The low energy electronic excitations are localized within the molecular entity and therefore they are neutral. Excitations of this kind are known as Frenkel excitons. The characteristic binding energy of these tight bound excitons can be as large as 2 eV and even more. As a result, the optical gap in molecular solid does not correspond to the energy of direct generation of e-h pairs, but to the energy of Frenkel excitons. Promotion of one electron between neighbouring molecules gives rise to a chargetransfer exciton (CTE). The energy of these states is higher than the optical gap. The identification of these levels has been made particularly difficult by the weak absorption intensity of the optical excitations due to the negligible overlap of the ground state wavefunction, which is localized on one molecule, and the excited state wavefunction, which extends over two or more molecules. Nevertheless, Stark spectroscopy allows us to identify CTE at energy higher than the optical gap (see Section 5). We assume therefore that in general the free-particle conduction band is at slightly higher energy than the CTEs. In this paper the selection rules for purely electronic transitions and the Herzberg-Teller (H-T) coupling mechanism for vibronic transitions will be reviewed. Photoluminescence investigation of high quality C6o single crystals shows that the emission activity is mostly controlled by surface or defect induced C6o X-traps, with the emission spectra consisting of several sub-spectra built on Tlg false origins. The lowest Frenkel exciton has been located by two-photon excitation spectroscopy at 1.85 eV and assigned to Tlg by the analysis of its H - T activity. The lowest charge-transfer state has been identified by electroabsorption spectroscopy at 2.45 eV, indicating that the bottom of the conduction band in solid C6o is at least 0.6 eV higher than the lowest localized Frenkel exciton.
2. Optical transition selection rules and H - T coupling Since the ground state of the free molecule is totally symmetric (Ag character), the low energy excitations are dipole forbidden since the lowest states transform like irreducible representations of gerade symmetry (T2g, Tlg, Gg, Hg) [911 ]. The only dipole allowed transition is from the ground state to states of T1, symmetry. There are several T1, ~ Ag transitions which have increasing oscillator strength by going towards higher energies. The region at about 2.00 eV was identified by many investigators [3-5,12,13] to be the region of forbidden transitions.
It is well known that selection rules of transitions from the ground state to excited states may be derived from the solution of the direct product of irreducible representation of the ground and excited state wavefunctions (wfs) and the electric dipole operator. The transition matrix element (~gLerl ~ ) is non-zero (where q)g and ~ are the ground and excited states, respectively, and er is the electric dipole operator) if the direct product contains the totally symmetric representation. Therefore: r'g@ rm@ re = Ag
(1)
where Fg is the representation of the ground state wf (Ag) and/'~ is the representation of the excited state wf. In the case of the/t, point group, the electric dipole operator Fro, transforms like the Tiu representation and the direct product for the transition from the ground state to Tlg does not contain Ag, making the transition matrix element equal to zero. In fact: AgQTlu@Tlg:#Ag
i.e.
(Ag[erlTlg)=0
(2)
The mechanism that is active in making these formally forbidden transitions, observable in absorption, is the H-T coupling [ 14]. Allowing the transition moment to depend on the nuclear normal coordinates Q, the transition from the ground state Ag to a vibronic level of the excited Tlg state, may acquire some intensity by borrowing it from higher energy allowed transitions (nlTlu ~ 1lAg). The H-T vibronic mechanism implies that transitions between two states may occur with a finite probability at nuclear coordinates away from the equilibrium geometry for particular normal coordinates of appropriate symmetry. The selection rule that governs the H-T vibronic coupling is the following: r'g @ Fm @ !'e @ r'v -- As
(3)
where cP~q~v is the total vibronic wf of the excited state ( ~ , = electronic wf; pv = vibrational wf) involved in the transition, and Fv is the representation of the vibrational wf. In the case in which Fg =As and -re = Tlg, the vibrations which are active in the H-T coupling belong to the symmetry representations a~, hu and hu. In the case, for instance, of vibration of tlu symmetry the total direct product is the following: Ag®Tlu ®Ttg® hu = Ag
(4)
and therefore the transition matrix element is non-zero: (Agl erl Tlgtlu) ¢ 0
(5)
In conclusion, while the purely electronic transition 11Tig ~ 1lag is still forbidden, the transition to the vibronic level Tlgtlu is allowed. This transition is called a 'false origin'. The electronic Hamiltonian Z can be expressed as 6,gf
+
.
M. Muccini / Synthetic Metals 83 (1996) 213-219
For small displacements, the second term of the Hamiltonian acts as a perturbation and QK is a normal coordinate. The adiabatic wfs of the excited state @ e ( q , Q ) , where q and Q are the electronic and nuclear coordinates, respectively, are expanded over diabatic zero-order wfs:
~ = ~c,~(Q) ~
(7)
i
The intensities of H - T active transitions to vibronic levels may therefore be calculated by evaluating the expansion coefficients c u. These have been calculated by Negri et al. [ 12] with a CNDO/S Hamiltonian. It turns out that the most active H - T mode in the case of l~T~g e- l~Ag transitions is t~ with 1440 c m - ~ vibrational frequency.
3. Photoexcitation trapping and fluorescence The photoluminescence properties of solid C6o have been investigated by many groups [ 5,15-18 ] and different microscopic interpretations of the fluorescence spectra, even for nominally equal morphologies, have been proposed. For solid C~o, the number of spectrally resolvable peaks obviously depends on the morphology of the C6o material. In fact, the spectrum of C6o film exhibits only broad emission bands at approximately 730 and 810 nm, while C6o single crystals show narrow and well-resolved lines (see Fig. 1). It is reasonable in the case of the film to assume that fluorescing C6o molecules are located in statistically varying environments leading to pronounced inhomogeneous broadening effects in the optical spectra. The number of resolvable fluorescence peaks increases in the case of the single crystal as a consequence of reduced inhomogeneous broadening of the individual optical transitions. In the case of the single crystal we find differing spectra. Fig. 1 shows three normalized photoluminescence spectra of crystalline C6o taken at low temperature. Well-resolved resonances are present in all the spectra but the number of peaks Energy [¢V] 1,4
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and the intensity distribution of the emission spectrum depend on the sample and on the spatial position of the laser excitation spot on the sample. This spatially inhomogeneous behaviour of the photoluminescence spectrum shows that inhomogeneously distributed crystal imperfections, such as chemical impurities or crystal defects, influence the emission process. Furthermore, by scanning the excitation spot on the sample the change in intensity for a particular photoluminescence peak is connected with a simultaneous change in intensity of a spectrally adjacent emission line. In other words, the spectrum seems to be composed of pairs of emission lines with energy separation of about 266 cm - 1. We suggest that each emission pair originates from C6o molecules in a particular crystal environment. C6o molecules adjacent to chemical impurities, to crystal defects or to crystal surfaces experience a different energetic shift of the electronic states resulting in different emission lines in the fluorescence spectrum. However, the defects do not change the characteristic vibronic structure of 'the emission of the adjacent C6o host molecule. Such defectrelated photoluminescence from host molecules is well known for anthracene single crystals [ 19-21] and is called X-traps (Fig. 2). Photogeneration ofsinglet excitons viaoneor two-photon absorption processes leads quickly ( 10-~3 s) to trapping of the excitations into the manifold of X-traps and to subsequent radiative emission. A more quantitative analysis of the single-crystal photoluminescence spectra can be obtained by considering the vibronic intensity borrowing activity of the Tig lowest excited electronic state (see Section 3 for its determination). As we mentioned above, the T~g false origin due to the tlu mode with 1440 c m - I vibrational frequency is expected to dominate both the absorption and the emission optical spectra. We :consider that each t~u related transition is split into two emission lines and that there is a totally symmetric ag progression built on it [12]. For each emission centre, the relative strengths of these three fluorescence lines are assumed to be 10:5:2. Taking into account an experimentally determined linewidth broadening of 22 meV for all emission lines, it is possible to simulate the fluorescence spectra as the superpos-
a)
A
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215
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,
,
,
,
i
. . . . . . . .
14000
15000
Wavenumber [cm"1]
Fig. 1. Normalized photolumineseence spectra of crystalline C6o at T= 10 K. The excitationenergyis 15 800 cm-1. The spectralshapedependson the sampleand on the position of the excitinglaser spot on the sample (see text for explanation).
c)
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Fig. 2. Schematic showing different X-traps due to (a) su_rfaceeffect, (b) chemical impurities, (c) oxygen impurities and (d) vacancies of molecules.
For each of these configurationsthereis a correspondinglocalizedelectronic level shifted with respect to the 0--0transition that still retains the characteristic vibronicstructure of the Cto molecule.
M. Muccini / Synthetic Metals 83 (1996) 213-219
216
Molecular symmetry Ih
Site symmetry $6
Ti~ T 2 g ~
~ Ao
Factor group symmetry
Th
Ao
(%x+e-W+%z)
Eo (%x+c~w-2%z,%x"aw)
G ~ E g ~ T g
(~, %=,a_~)
Fig. 3. Correlationdiagram for the lowest three excited states of C6o.The [h point group of the isolated Cs0 moIecule(left column) correlatesvia the S~ site symmetry(centre) with the Thfactorgroup for solid Ca (right column).
ition of the 'sub-spectra' of all active emission centres [22]. In order to account for the different spectral shapes we vary the contribution, i.e., the overall strength of each 'sub-spectrum' that is related to the relative concentration of X-traps. The reproducibility of the main features of the experimental spectra is a direct confirmation of the validity of this interpretation.
4. Experimental determination of the optical gap
As already mentioned above, electronic levels of the isolated molecule belong to the irreducible representation of the Ih point group and the lowest singlet excited states (T~g, Tag, Gg) [9-11 ] are formally one-photon forbidden. Two-photon selection rules may be derived directly from the character table of the molecular point group. A transition to an excited state belonging to the irreducible representation ~ is two-photon allowed if the representation transforms like the polarizability tensor components. Thus, in the isolated molecule, the lowest Frenkel excitons are both one-photon and two-photon forbidden (see Fig. 3). In the solid, the crystal wavefunctions (wfs) that are generated as a linear combination of molecular wfs of the molecules in the unit cell form a basis for the irreducible representation of the factor group, which is isomorphous with the space group [7,8]. From X-ray diffraction analysis [23,24] we i~mowthat C6o possesses at low temperature a simple cubic (sc) phase with four inequivalent C6o molecules in the unit cell, belonging to the Th space group. The electronic states Of crystal C6o are therefore classified according to the irreducible representations of the Th point group. The correlation among the symmetry of the free molecular wfs and the symmetry of the crystal wfs depends on the symmetry operations of the factor group that are retained by the molecules in the crystal. These form a group in itself which is a sub-group of both the factor group and the molecular point group and is defined as the site group. In the case
of C6o, due to the high symmetry of the cubic packing, the site group in the low temperature phase is $6. The correlation diagram for the lowest excited singlet states is reported in Fig. 3. Each molecular irreducible representation (right-hand side of Fig. 3) correlates via the site group symmetry (centre of Fig. 3) to the irreducible representation of the factor group (left-hand side of Fig. 3) by preserving the parity character. In particular the Ttg molecular irreducible representation correlates with the Ag, Eg and Tg irreducible representation of the factor group. Since these representations transform in the Th factor group like polarizability tensor components, the Ttg level, which is two-photon forbidden in the free molecule, splits in the crystal and becomes partially allowed. This correlation effect is also known as the crystal field effect. By using this effect it is therefore possible to locate directly the lowest forbidden singlet by two-photon excitation (TPE) in solid C~o. In Fig. 4 we show one-photon absorption and two-photon excitation spectra of crystalline C~o taken at low temperature. Since the lowest singlet excitons are partially dipole allowed in two-photon absorption, the onset of the TPE spectrum at O-O tl u
"
TPE " - .
J 14000
15000
16000
17000
18000
Wavenumber[cm"l] Fig. 4. Two-photonexcitation (TPE) spectrumand absorption(ABS) spectrumof crystallineC6oat T= 4 K. The verticalarrowshowsthe lowestpurely electronic transition at 14 880 cm- 1. The energy of the qu phonon mode involvedin the H-T couplingis shown as a horizontal arrow.
217
M. Muccini / Synthetic Metals 83 (1996) 213-219
14 880 c m - 1 unambiguously marks the lowest purely electronic transition of crystalline C6o. Also, the one-photon absorption (ABS) spectrum shows its energetically lowest weak resonance at 14 880 c m - i . The fact that g-g purely electronic transitions are observable in one-photon spectra means that the optical transitions are not completely forbidden. We assume that either disorder-induced distortions of the icosahedral symmetry of the C6o molecules lead to a nonvanishing dipole transition strength or that the weak 0-0 onephoton resonance is due to quadrupole transition strength. However, there is no measurable signal below the onset at 14 880 c m - x. We can now assign the character of the lowest 0-0 transition from its H - T activity. We already mentioned that in the case of the Tlg level according to Negri et al. calculations [ 12] the transition induced by the tiu vibration with 1440 c m - i vibrational frequency is expected to dominate the optical spectra. Accordingly, an absorption resonance linked to the bulk transition is expected when the photon energy is equal to the 0-43 transition energy plus the energy of the vibrational mode. The energy shift between the 0-0 band and the main peak in the low energy region of the absorption spectrum gives indeed a direct indication that the lowest forbidden Frenkel exciton in C6o single crystal is Tig at 14 880 c m - 1.
5. Charge-transfer states and free carrier generation energy As mentioned above, in the solid the absorption spectrum is dominated by intramolecular excitations. Nevertheless, the discrepancy at around 2.5 eV where the absorption in the solid is more intense than in the isolated molecule is rather puzzling. Tsubo and Nasu [25] separated the intra- and intermolecular contributions to the Hamiltonian, and predicted that the increased spectral weight in the region of 2.5 eV is due to intermolecular interactions leading to charge transfer excitons. Such charge-transfer excitations are expected to be the dominant precursor of the photocarrier generation since the charges are delocalized on different molecular sites with a decreased binding energy compared to Frenkel excitons. Photoconductivity experiments show indeed a symbatic behaviour of the action spectrum with co [26] which is hard to rationalize in terms of band-to-band transitions. Moreover, photocurrent measurements show a sharp increase of the photocarrier-generation efficiency above 2.3 eV which was interpreted in terms of excitation processes involving intermolecular charge-transfer states [ 27 ]. Shirley et al. [ 28 ] using a model Hamiltonian predicted that charge-transfer states are located just below the conduction band which was experimentally determined by PES and IPES to be 2.3 + 0.1 eV above the valence band [29]. Despite these strong indications the existence of such charge-transfer excitons still needs to be unambiguously confirmed. Electroabsorption can in principle give precise
indications on the nature of the photoexcitations in molecular crystals. In fact, absorption bands originating from different electronic transitions behave differently under the influence of an electric field and one can properly assign localized neutral excitations, charge-transfer states, and band-to-band transitions [30-34]. The energy shift AE of an electronic transition induced by an electric field F is given by A E = A / x F + 1/2 Ac~F 2
(8)
where A/x=/xe-/xg and A a = % - a g are the change in dipole moment and polarizability in exciting an electron from the ground state (g) to an excited state (e). Using the Liptay theory [35] for isotropic media the corresponding fieldinduced absorption AAeff is
AAeff(2w)=~l/zFeff[~c-~u+l'~c2"~2] 2 [A a 8A
A ],,.L2
82A~
(9)
where A is the optical absorbance, h is Planck's constant, c is the velocity of light, and u is the frequency. F~rf is the local field in the Lorentz approximation. Frenkel excitons are localized on a single molecule and, since the molecule is centrosymmetric, they are not accompanied by a change of the molecular dipole moment upon excitation (A/z = 0). The energy shift induced by the electric field is therefore given only by the second-order Stark effect ( A E = 1/2 A a F 2) and the electroabsorption spectrum is proportional to the first derivative of the absorption spectrum. The change in polarizability A a is an indication of the Frenkel exciton delocalization distance. In the case of charge-transfer excitons a photon promotes an electron from one molecule to another localized at the neighbouring or at a more distant site. The bound electronhole pair has a large dipole moment A/~ = 10-30 Debye and the field-induced shift is mainly due to the first-order Stark effect A E = A/x F. For an isotropic orientational distribution of molecules the electric field induces a broadening of the absorption band and the electroabsorption spectrum follows the second derivative of the absorption (see Eq. (9)) [3136]. In some materials the neutral and charge-transfer (or bandto-band) transitions occur at the same energy and the electric field can mix the different states. The electric field induces the borrowing of both the oscillator strength and polarity from one band to another. Therefore in such cases the electroabsorption spectrum can have a very complex shape. Electroabsorption spectroscopy was performed on a C6o thin film to study the electrical properties (dipole moments and polarizabilities) of the optically excited states. To do this we modelled the absorption spectrum as a series of purely electronic transitions (i.e. Gaussian absorption profiles), and then we fitted the electroabsorption spectrum with a weighted sum of the first and second derivatives of each Gaussian (Eq. (9)) to find the parameters A a and A/x for each transition. The energetical positions of the Gaussian bands were chosen following the CNDO/S calculation by Negri et al. [ 12] (see Table 1).
218
M. Muccini / Synthetic Metals 83 (1996) 213-219 3x104
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Wavenumber (cm -1) Fig. 5. Electroabsorptionspectrumat T= 4 K (continuouscurve) and the resultof its fitting(dotted curve) withthe firstand secondderivativesof the Gaussian bands correspondingto the calculatedelectronictransitions.
Table 1 Energies of the lowest electronicstates of C6ocalculatedby CNDO/S with different configurationinteractions (from Ref. [12];f ° is the calculated oscillator strength) Symmetry
CI size 14× 14 E (eV)
1T2g 1Tlg 1Gg 1Hg 1T2u 1Hu 1Gu 1Ttu 2G,, 2Hu
2.31 2.35 2.40 2.72 2.93 3.13 3.18 3.49 3.54 3.77
2Ttu 3TI,, 4Ttu 5Ttu 6TI,~ 7TI,, 8Tlu 9T1~ 10Tlu 11TI,, 12Tlu 13Ttu 14Tlu
4.08 5.02 5.34 5.84
28 × 30 fc
0.21
0.15 9.06 3.60 14.2
E (eV) 2.29 2.33 2.34 2.66 2.77 3.02 3.12 3.40 3.43 3.72 4.02 4.28 4.64 5.03 5.20 5.51 5.62 6.31 6.54 6.61 6.71 7.24
35 × 37 f¢
0.12
0.54 2.70 0.54 2.94 5.79 0.81 3.21 0.42 0.57 0.39 0.03 0.99
E (eV) 2.29 2.33 2.34 2.65 2.76 3.01 3.11 3.36 3.38 3.70 4.00 4.26 4.59 4.97 5.49 5.57 6.27 6.50 6.56 6.69 6.73 6.83 7.21
f°
and 790 × 10- 24 cm 3, respectively. It is known that A/~ values as large as 10 Debye correspond to charge-transfer states where the distance between the charges is that of two neighbouring C~o molecule centres. This means that the exciton at 2.45 eV has a strong charge-transfer character and that the bound electron-hole pair is delocalized on two neighbouring molecules. By assuming that the low edge of the conduction band is at a slightly higher energy than the delocalized charge-transfer states we derive that free carriers are generated when exciting with 0.6 eV energy in excess with respect to the optical gap.
Acknowledgements 0.12
0.63 2.46 0.75 4.83 0.90 1.35 0.24 0.48 0.17 0.09 0.03 0.03 0.84
The result of the fitting is reported in Fig. 5, showing that all the main spectral features of the electroabsorption spectrum are reproduced. The calculated parameters A/x and A c~ for the electronic transition located at 2.45 eV ( 19 760 cm - 1) are 11.3 Debye
This paper contains work which has been done in collaboration with C. Taliani, R. Zamboni, H. Schlaich, J. Feldmann and L.M. Blinov. The skillful technical assitance ofP. Mei is greatfutly acknowledged, as well as financial support by the European Community Basic Research Action Esprit 8013LEDFOS Project.
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M. Muccini / Synthetic Metals 83 (1996) 213-219 [7] A.S. Davydov, Theory of Molecular Excitons, Plenum, New York, 1971. [8] D.P. Craig and S.H. Walmsley, Exciton in Molecular Crystals, Benjamin, New York, 1968. [9] F. Negri, G. Orlandi and F. Zerbetto, Chem. Phys. Lett., 144 (1988) 31. [10] I. Laszlo and L. Udvardi, Chem. Phys. Lett., 136 (1987) 418. [ 11] I. Laszlo and L. Udvardi, J. Mol. Struct., 183 (1989) 271. [ 12] F. Negri, G. Orlandi and F. Zerbetto, J. Chem. Phys., 97 (1992) 6496. [13] K. Yaban and G.F. Bertseh, Chem. Phys. Lett., 197 (1992) 32. [ 14] G. Herzberg and E. Teller, Z. Phys. Chem. B, 21 (1933) 410. [15] P.A. Lane, L.S. Swanson, Q.X. Ni, J. Shinar, J.P. Enget, T.J. Barton and L. Jones, Phys. Rev. Lett., 68 (1992) 887. [16] M. Matus, H. Kuzmany and E. Sohmen, Phys. Rev. Lett., 68 (1992) 2822. [17] J. Feldman, R. Fischer, W. Guss, E.O. Goebel, S. Schmitt-Rink and W. Kraetchmer, Europhys. Lett., 20 (1992) 553. [18] E. Shin, J.H. Park, M.Y. Lee, D.H. Kim, Y.D. Such, S.I. Yang, S.M. Jin and S.K. Kim, Chem. Phys. Lett., 209 (1993) 427. [19] A. Brillante, D.P. Craig, A.W.H. Mau and J. Rajikan, Chem. Phys. Lett., 31 (1975) 215. [20] V.A. Lisovenko, M.T. Shpak and V.G. Antoniuk, Chem. Phys. Lett., 42 (1976) 339. [21 ] D.P. Craig and J. Rajikan, J. Chem. Soc., Faraday Trans. 2, 74 (1978) 292.
219
[22] W. Guss, J. Feldmann, E.O. Goebel and C. Taliani, Phys. Rev. Lett., 72 (1994) 2644. [23] P.A. Heiney, J.E. Fischer, A.R. McGhie, W.J. Romanow, A.M. Denenstein, J.P. McCauley, Jr., A.B. Smith III and D.E. Cox, Phys. Rev. Lett., 67 (1991) 1468. [24] P.A. Heiney, J.E. Fischer, A.R. McGhie, Jr., A.B. Smith III and D.E. Cox, Phys. Rev. Lett., 66 (1991) 2911. [25] T. Tsubo and K. Nasu, Solid State Commun., 91 (1994) 907. [26] S. Kazaoui, R. Ross and N. Minami, Phys. Rev. B, 52 (1995) R11 665. [27] S. Kazaoui, R. Ross and N. Minami, SolidState Commun., 90 (1994) 623. [28] E.L. Shirley, L.X. Benedict and S.G. Louie, Phys. Rev. B, submitted for publication. [29] R.W. Lof, M.A. van Veenendaal, B. Koopmans, H.T. Jonkman and G.A. Sawatzky, Phys. Rev. Lett., 68 (1992) 3924. [30] L.M. Blinov and N.A. Kirichenko, Fiz. Tverd. Tela (Leningrad), 14 (1972) 2489. [31] L. Sebastian and H. Bgssler, Chem. Phys., 61 (1981) 125. [32] L. Sebastian and G. Weiser, Chem. Phys., 62 (1981) 447. [33] G. Weiser, Phys. Rev. B, 45 (1992) 14 076. [34] A. Horvath, H. B~sler and G. Weiser, Phys. Status Solidi (b), 173 (1992) 755. [35] W. Liptay, in O. Sinanoghi (ed.), Modern Quantum Chemistry, Academic Press, New York, 1945, p. 45. [36] L.M. Blinov, Sov. Sci. Rev., 12 (1989) 1-3.
Synthetic Metals 83 (1996) 213-219
Optical properties of solid C6o M. M u c c i n i * Istituto di Spettroscopia Molecolare del CNR, via Gobetti 101, 1-40129 Bologna, Italy
Abstract The opticai properties of materials are strongly related to the nature of the photoexcitations in the solid. FuIlerene C6o in the solid state is a typical molecular material in which the molecules are weakly held together by van der Waals forces and the electronic excitations are very close in energy and nature to those of the free molecule. The lowest electronic states in solid C6o are dipole forbidden and can be described as tight bound (Frenkel) excitons. Optical emission of C6o single crystals can be explained in terms of photoluminescence sub-spectra built on vibronically allowed false origins. Further to these neutral excitations which determine the optical gap there are charged excitations corresponding to the promotion of electrons from ball to ball and from ball to the free electron continuum. We observe intermolecuIar chargetransfer excitons by measuring the electroabsorption of thin films at liquid helium temperature. The energy necessary to generate directly the electron-hole (e-h) pairs is set at least 0.6 eV higher than the optical gap. Keywords: Fullerene; Optical properties
1. Introduction Since fullerene C6o has become available in macroscopic quantities there has been an ongoing experimental and theoretical effort to understand its electronic and optical properties. The electronic energetics of molecular C6o is determined by the 60 electrons on p orbitals, one on each carbon atom, while the cage is formed by the overlap of sp 2 hybridized orbitals. Each p orbital makes a small angle with adjacent orbitals (23.2°). The overlap between orbitals allows therefore the formation of an extended n'r electronic system. Using the one-electron description of the electronic structure, according to the Htickel molecular orbital approach, one gets a closed shell system with a considerable gap between HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) orbitals. Furthermore, the high symmetry of the molecule gives rise to a large degeneracy of the molecular orbitals. Electronic promotion from HOMO (hu) to LUMO (tlu) is forbidden for electric dipole operator and, therefore, it is forbidden for linear optical absorption, while promotions from HOMO - I (gg, hg) to LUMO and HOMO to LUMO + 1 (txg) are allowed. The theoretical investigation of a more rigorous treatment of the electronic structure should include Coulomb interactions. In fact, in "rr conjugated molecules, it has been recog* Corresponding author. Fax: +39 51 639 8539. 0379-6779/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved P//S0379-6779 (96)04472-4
nized long ago [ 1] that inclusion of e-e correlation is essential to reproduce the low energy excitations. In the multielectron approach, the electronic states are classified according to the molecular point group which, in the case of the hycosahedral C6o molecule, is Ih. The molecular nature of solid C6o is well established by the many experimental results of the last few years. One of the most convincing evidence is given by the electronic absorption spectrum. The spectrum of a thin film was reported for the first time by Kr~itschmer et al. [2]. The absorption spectrum consists of a very weak and broad system extending from 1.9 to 2.7 eV (650-450 nm) and of a series of sharp bands at 3.65 eV (339 nm), 4.70 eV (264 nm) and 5.74 eV (216 nm). The solution spectrum [3] is very similar to the solid spectrum [2,4,5] and has been analysed in terms of Herzberg-Teller vibronic coupling (see Section 2). The similarity between the spectra of isolated molecules and the solid implies that the intermolecular interactions are weak, due to van der Waals forces and, therefore, the solid is a typical molecular crystal. B and-structure calculation in the local density approximation (LDA) gives a value of about 1 eV for the optical gap [6], significantly different from that obtained by photoemission spectroscopy (PES) and inverse photoemission spectroscopy (IPES) which results in a factor of two larger. The many-electron effects are taken into account in the quasi-particle approach, leading to a gap and to HOMO and LUMO bandwidths in agreement with the photoemission data.
214
M. Muccini /Synthetic Metals 83 (1996) 213-219
Localized electronic excitations and weak intermolecular interactions constitute the main ingredients for the description of the low energy electronic excitations in molecular solids. Major contributions to this field have been given by Davydov [7 ] and Craig and Walmsley [ 8]. Intermolecular interaction in the solid causes a shift of energy in the electronic levels of the free molecule and a spreading of the levels into bands, whose widths depend on the interaction between translationally non-equivalent molecules [ 7 ]. The low energy electronic excitations are localized within the molecular entity and therefore they are neutral. Excitations of this kind are known as Frenkel excitons. The characteristic binding energy of these tight bound excitons can be as large as 2 eV and even more. As a result, the optical gap in molecular solid does not correspond to the energy of direct generation of e-h pairs, but to the energy of Frenkel excitons. Promotion of one electron between neighbouring molecules gives rise to a chargetransfer exciton (CTE). The energy of these states is higher than the optical gap. The identification of these levels has been made particularly difficult by the weak absorption intensity of the optical excitations due to the negligible overlap of the ground state wavefunction, which is localized on one molecule, and the excited state wavefunction, which extends over two or more molecules. Nevertheless, Stark spectroscopy allows us to identify CTE at energy higher than the optical gap (see Section 5). We assume therefore that in general the free-particle conduction band is at slightly higher energy than the CTEs. In this paper the selection rules for purely electronic transitions and the Herzberg-Teller (H-T) coupling mechanism for vibronic transitions will be reviewed. Photoluminescence investigation of high quality C6o single crystals shows that the emission activity is mostly controlled by surface or defect induced C6o X-traps, with the emission spectra consisting of several sub-spectra built on Tlg false origins. The lowest Frenkel exciton has been located by two-photon excitation spectroscopy at 1.85 eV and assigned to Tlg by the analysis of its H - T activity. The lowest charge-transfer state has been identified by electroabsorption spectroscopy at 2.45 eV, indicating that the bottom of the conduction band in solid C6o is at least 0.6 eV higher than the lowest localized Frenkel exciton.
2. Optical transition selection rules and H - T coupling Since the ground state of the free molecule is totally symmetric (Ag character), the low energy excitations are dipole forbidden since the lowest states transform like irreducible representations of gerade symmetry (T2g, Tlg, Gg, Hg) [911 ]. The only dipole allowed transition is from the ground state to states of T1, symmetry. There are several T1, ~ Ag transitions which have increasing oscillator strength by going towards higher energies. The region at about 2.00 eV was identified by many investigators [3-5,12,13] to be the region of forbidden transitions.
It is well known that selection rules of transitions from the ground state to excited states may be derived from the solution of the direct product of irreducible representation of the ground and excited state wavefunctions (wfs) and the electric dipole operator. The transition matrix element (~gLerl ~ ) is non-zero (where q)g and ~ are the ground and excited states, respectively, and er is the electric dipole operator) if the direct product contains the totally symmetric representation. Therefore: r'g@ rm@ re = Ag
(1)
where Fg is the representation of the ground state wf (Ag) and/'~ is the representation of the excited state wf. In the case of the/t, point group, the electric dipole operator Fro, transforms like the Tiu representation and the direct product for the transition from the ground state to Tlg does not contain Ag, making the transition matrix element equal to zero. In fact: AgQTlu@Tlg:#Ag
i.e.
(Ag[erlTlg)=0
(2)
The mechanism that is active in making these formally forbidden transitions, observable in absorption, is the H-T coupling [ 14]. Allowing the transition moment to depend on the nuclear normal coordinates Q, the transition from the ground state Ag to a vibronic level of the excited Tlg state, may acquire some intensity by borrowing it from higher energy allowed transitions (nlTlu ~ 1lAg). The H-T vibronic mechanism implies that transitions between two states may occur with a finite probability at nuclear coordinates away from the equilibrium geometry for particular normal coordinates of appropriate symmetry. The selection rule that governs the H-T vibronic coupling is the following: r'g @ Fm @ !'e @ r'v -- As
(3)
where cP~q~v is the total vibronic wf of the excited state ( ~ , = electronic wf; pv = vibrational wf) involved in the transition, and Fv is the representation of the vibrational wf. In the case in which Fg =As and -re = Tlg, the vibrations which are active in the H-T coupling belong to the symmetry representations a~, hu and hu. In the case, for instance, of vibration of tlu symmetry the total direct product is the following: Ag®Tlu ®Ttg® hu = Ag
(4)
and therefore the transition matrix element is non-zero: (Agl erl Tlgtlu) ¢ 0
(5)
In conclusion, while the purely electronic transition 11Tig ~ 1lag is still forbidden, the transition to the vibronic level Tlgtlu is allowed. This transition is called a 'false origin'. The electronic Hamiltonian Z can be expressed as 6,gf
+
.
M. Muccini / Synthetic Metals 83 (1996) 213-219
For small displacements, the second term of the Hamiltonian acts as a perturbation and QK is a normal coordinate. The adiabatic wfs of the excited state @ e ( q , Q ) , where q and Q are the electronic and nuclear coordinates, respectively, are expanded over diabatic zero-order wfs:
~ = ~c,~(Q) ~
(7)
i
The intensities of H - T active transitions to vibronic levels may therefore be calculated by evaluating the expansion coefficients c u. These have been calculated by Negri et al. [ 12] with a CNDO/S Hamiltonian. It turns out that the most active H - T mode in the case of l~T~g e- l~Ag transitions is t~ with 1440 c m - ~ vibrational frequency.
3. Photoexcitation trapping and fluorescence The photoluminescence properties of solid C6o have been investigated by many groups [ 5,15-18 ] and different microscopic interpretations of the fluorescence spectra, even for nominally equal morphologies, have been proposed. For solid C~o, the number of spectrally resolvable peaks obviously depends on the morphology of the C6o material. In fact, the spectrum of C6o film exhibits only broad emission bands at approximately 730 and 810 nm, while C6o single crystals show narrow and well-resolved lines (see Fig. 1). It is reasonable in the case of the film to assume that fluorescing C6o molecules are located in statistically varying environments leading to pronounced inhomogeneous broadening effects in the optical spectra. The number of resolvable fluorescence peaks increases in the case of the single crystal as a consequence of reduced inhomogeneous broadening of the individual optical transitions. In the case of the single crystal we find differing spectra. Fig. 1 shows three normalized photoluminescence spectra of crystalline C6o taken at low temperature. Well-resolved resonances are present in all the spectra but the number of peaks Energy [¢V] 1,4
1,5 L
1.6 i
1.7 i
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i I
t
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and the intensity distribution of the emission spectrum depend on the sample and on the spatial position of the laser excitation spot on the sample. This spatially inhomogeneous behaviour of the photoluminescence spectrum shows that inhomogeneously distributed crystal imperfections, such as chemical impurities or crystal defects, influence the emission process. Furthermore, by scanning the excitation spot on the sample the change in intensity for a particular photoluminescence peak is connected with a simultaneous change in intensity of a spectrally adjacent emission line. In other words, the spectrum seems to be composed of pairs of emission lines with energy separation of about 266 cm - 1. We suggest that each emission pair originates from C6o molecules in a particular crystal environment. C6o molecules adjacent to chemical impurities, to crystal defects or to crystal surfaces experience a different energetic shift of the electronic states resulting in different emission lines in the fluorescence spectrum. However, the defects do not change the characteristic vibronic structure of 'the emission of the adjacent C6o host molecule. Such defectrelated photoluminescence from host molecules is well known for anthracene single crystals [ 19-21] and is called X-traps (Fig. 2). Photogeneration ofsinglet excitons viaoneor two-photon absorption processes leads quickly ( 10-~3 s) to trapping of the excitations into the manifold of X-traps and to subsequent radiative emission. A more quantitative analysis of the single-crystal photoluminescence spectra can be obtained by considering the vibronic intensity borrowing activity of the Tig lowest excited electronic state (see Section 3 for its determination). As we mentioned above, the T~g false origin due to the tlu mode with 1440 c m - I vibrational frequency is expected to dominate both the absorption and the emission optical spectra. We :consider that each t~u related transition is split into two emission lines and that there is a totally symmetric ag progression built on it [12]. For each emission centre, the relative strengths of these three fluorescence lines are assumed to be 10:5:2. Taking into account an experimentally determined linewidth broadening of 22 meV for all emission lines, it is possible to simulate the fluorescence spectra as the superpos-
a)
A
£
/-
215
'
,
,
,
,
i
. . . . . . . .
14000
15000
Wavenumber [cm"1]
Fig. 1. Normalized photolumineseence spectra of crystalline C6o at T= 10 K. The excitationenergyis 15 800 cm-1. The spectralshapedependson the sampleand on the position of the excitinglaser spot on the sample (see text for explanation).
c)
@@@@@@
@@@@@@@@
t
Fig. 2. Schematic showing different X-traps due to (a) su_rfaceeffect, (b) chemical impurities, (c) oxygen impurities and (d) vacancies of molecules.
For each of these configurationsthereis a correspondinglocalizedelectronic level shifted with respect to the 0--0transition that still retains the characteristic vibronicstructure of the Cto molecule.
M. Muccini / Synthetic Metals 83 (1996) 213-219
216
Molecular symmetry Ih
Site symmetry $6
Ti~ T 2 g ~
~ Ao
Factor group symmetry
Th
Ao
(%x+e-W+%z)
Eo (%x+c~w-2%z,%x"aw)
G ~ E g ~ T g
(~, %=,a_~)
Fig. 3. Correlationdiagram for the lowest three excited states of C6o.The [h point group of the isolated Cs0 moIecule(left column) correlatesvia the S~ site symmetry(centre) with the Thfactorgroup for solid Ca (right column).
ition of the 'sub-spectra' of all active emission centres [22]. In order to account for the different spectral shapes we vary the contribution, i.e., the overall strength of each 'sub-spectrum' that is related to the relative concentration of X-traps. The reproducibility of the main features of the experimental spectra is a direct confirmation of the validity of this interpretation.
4. Experimental determination of the optical gap
As already mentioned above, electronic levels of the isolated molecule belong to the irreducible representation of the Ih point group and the lowest singlet excited states (T~g, Tag, Gg) [9-11 ] are formally one-photon forbidden. Two-photon selection rules may be derived directly from the character table of the molecular point group. A transition to an excited state belonging to the irreducible representation ~ is two-photon allowed if the representation transforms like the polarizability tensor components. Thus, in the isolated molecule, the lowest Frenkel excitons are both one-photon and two-photon forbidden (see Fig. 3). In the solid, the crystal wavefunctions (wfs) that are generated as a linear combination of molecular wfs of the molecules in the unit cell form a basis for the irreducible representation of the factor group, which is isomorphous with the space group [7,8]. From X-ray diffraction analysis [23,24] we i~mowthat C6o possesses at low temperature a simple cubic (sc) phase with four inequivalent C6o molecules in the unit cell, belonging to the Th space group. The electronic states Of crystal C6o are therefore classified according to the irreducible representations of the Th point group. The correlation among the symmetry of the free molecular wfs and the symmetry of the crystal wfs depends on the symmetry operations of the factor group that are retained by the molecules in the crystal. These form a group in itself which is a sub-group of both the factor group and the molecular point group and is defined as the site group. In the case
of C6o, due to the high symmetry of the cubic packing, the site group in the low temperature phase is $6. The correlation diagram for the lowest excited singlet states is reported in Fig. 3. Each molecular irreducible representation (right-hand side of Fig. 3) correlates via the site group symmetry (centre of Fig. 3) to the irreducible representation of the factor group (left-hand side of Fig. 3) by preserving the parity character. In particular the Ttg molecular irreducible representation correlates with the Ag, Eg and Tg irreducible representation of the factor group. Since these representations transform in the Th factor group like polarizability tensor components, the Ttg level, which is two-photon forbidden in the free molecule, splits in the crystal and becomes partially allowed. This correlation effect is also known as the crystal field effect. By using this effect it is therefore possible to locate directly the lowest forbidden singlet by two-photon excitation (TPE) in solid C~o. In Fig. 4 we show one-photon absorption and two-photon excitation spectra of crystalline C~o taken at low temperature. Since the lowest singlet excitons are partially dipole allowed in two-photon absorption, the onset of the TPE spectrum at O-O tl u
"
TPE " - .
J 14000
15000
16000
17000
18000
Wavenumber[cm"l] Fig. 4. Two-photonexcitation (TPE) spectrumand absorption(ABS) spectrumof crystallineC6oat T= 4 K. The verticalarrowshowsthe lowestpurely electronic transition at 14 880 cm- 1. The energy of the qu phonon mode involvedin the H-T couplingis shown as a horizontal arrow.
217
M. Muccini / Synthetic Metals 83 (1996) 213-219
14 880 c m - 1 unambiguously marks the lowest purely electronic transition of crystalline C6o. Also, the one-photon absorption (ABS) spectrum shows its energetically lowest weak resonance at 14 880 c m - i . The fact that g-g purely electronic transitions are observable in one-photon spectra means that the optical transitions are not completely forbidden. We assume that either disorder-induced distortions of the icosahedral symmetry of the C6o molecules lead to a nonvanishing dipole transition strength or that the weak 0-0 onephoton resonance is due to quadrupole transition strength. However, there is no measurable signal below the onset at 14 880 c m - x. We can now assign the character of the lowest 0-0 transition from its H - T activity. We already mentioned that in the case of the Tlg level according to Negri et al. calculations [ 12] the transition induced by the tiu vibration with 1440 c m - i vibrational frequency is expected to dominate the optical spectra. Accordingly, an absorption resonance linked to the bulk transition is expected when the photon energy is equal to the 0-43 transition energy plus the energy of the vibrational mode. The energy shift between the 0-0 band and the main peak in the low energy region of the absorption spectrum gives indeed a direct indication that the lowest forbidden Frenkel exciton in C6o single crystal is Tig at 14 880 c m - 1.
5. Charge-transfer states and free carrier generation energy As mentioned above, in the solid the absorption spectrum is dominated by intramolecular excitations. Nevertheless, the discrepancy at around 2.5 eV where the absorption in the solid is more intense than in the isolated molecule is rather puzzling. Tsubo and Nasu [25] separated the intra- and intermolecular contributions to the Hamiltonian, and predicted that the increased spectral weight in the region of 2.5 eV is due to intermolecular interactions leading to charge transfer excitons. Such charge-transfer excitations are expected to be the dominant precursor of the photocarrier generation since the charges are delocalized on different molecular sites with a decreased binding energy compared to Frenkel excitons. Photoconductivity experiments show indeed a symbatic behaviour of the action spectrum with co [26] which is hard to rationalize in terms of band-to-band transitions. Moreover, photocurrent measurements show a sharp increase of the photocarrier-generation efficiency above 2.3 eV which was interpreted in terms of excitation processes involving intermolecular charge-transfer states [ 27 ]. Shirley et al. [ 28 ] using a model Hamiltonian predicted that charge-transfer states are located just below the conduction band which was experimentally determined by PES and IPES to be 2.3 + 0.1 eV above the valence band [29]. Despite these strong indications the existence of such charge-transfer excitons still needs to be unambiguously confirmed. Electroabsorption can in principle give precise
indications on the nature of the photoexcitations in molecular crystals. In fact, absorption bands originating from different electronic transitions behave differently under the influence of an electric field and one can properly assign localized neutral excitations, charge-transfer states, and band-to-band transitions [30-34]. The energy shift AE of an electronic transition induced by an electric field F is given by A E = A / x F + 1/2 Ac~F 2
(8)
where A/x=/xe-/xg and A a = % - a g are the change in dipole moment and polarizability in exciting an electron from the ground state (g) to an excited state (e). Using the Liptay theory [35] for isotropic media the corresponding fieldinduced absorption AAeff is
AAeff(2w)=~l/zFeff[~c-~u+l'~c2"~2] 2 [A a 8A
A ],,.L2
82A~
(9)
where A is the optical absorbance, h is Planck's constant, c is the velocity of light, and u is the frequency. F~rf is the local field in the Lorentz approximation. Frenkel excitons are localized on a single molecule and, since the molecule is centrosymmetric, they are not accompanied by a change of the molecular dipole moment upon excitation (A/z = 0). The energy shift induced by the electric field is therefore given only by the second-order Stark effect ( A E = 1/2 A a F 2) and the electroabsorption spectrum is proportional to the first derivative of the absorption spectrum. The change in polarizability A a is an indication of the Frenkel exciton delocalization distance. In the case of charge-transfer excitons a photon promotes an electron from one molecule to another localized at the neighbouring or at a more distant site. The bound electronhole pair has a large dipole moment A/~ = 10-30 Debye and the field-induced shift is mainly due to the first-order Stark effect A E = A/x F. For an isotropic orientational distribution of molecules the electric field induces a broadening of the absorption band and the electroabsorption spectrum follows the second derivative of the absorption (see Eq. (9)) [3136]. In some materials the neutral and charge-transfer (or bandto-band) transitions occur at the same energy and the electric field can mix the different states. The electric field induces the borrowing of both the oscillator strength and polarity from one band to another. Therefore in such cases the electroabsorption spectrum can have a very complex shape. Electroabsorption spectroscopy was performed on a C6o thin film to study the electrical properties (dipole moments and polarizabilities) of the optically excited states. To do this we modelled the absorption spectrum as a series of purely electronic transitions (i.e. Gaussian absorption profiles), and then we fitted the electroabsorption spectrum with a weighted sum of the first and second derivatives of each Gaussian (Eq. (9)) to find the parameters A a and A/x for each transition. The energetical positions of the Gaussian bands were chosen following the CNDO/S calculation by Negri et al. [ 12] (see Table 1).
218
M. Muccini / Synthetic Metals 83 (1996) 213-219 3x104
',
....
, ....
, ....
t ....
I ....
, ....
, ....
,'
2x10 4
lx10 4
0 .°oO
-lx10 4
-2x10 4
-3x10 4 I
I
,
,
,
16000
,
I
,
,
,
20000
,
I
,
,
,
26000
,
I
I
30000
'
'
'
I
,
,
35000
,
,
I
,
,
,
40000
,
I
,
45000
,
,
,
I
J
60000
Wavenumber (cm -1) Fig. 5. Electroabsorptionspectrumat T= 4 K (continuouscurve) and the resultof its fitting(dotted curve) withthe firstand secondderivativesof the Gaussian bands correspondingto the calculatedelectronictransitions.
Table 1 Energies of the lowest electronicstates of C6ocalculatedby CNDO/S with different configurationinteractions (from Ref. [12];f ° is the calculated oscillator strength) Symmetry
CI size 14× 14 E (eV)
1T2g 1Tlg 1Gg 1Hg 1T2u 1Hu 1Gu 1Ttu 2G,, 2Hu
2.31 2.35 2.40 2.72 2.93 3.13 3.18 3.49 3.54 3.77
2Ttu 3TI,, 4Ttu 5Ttu 6TI,~ 7TI,, 8Tlu 9T1~ 10Tlu 11TI,, 12Tlu 13Ttu 14Tlu
4.08 5.02 5.34 5.84
28 × 30 fc
0.21
0.15 9.06 3.60 14.2
E (eV) 2.29 2.33 2.34 2.66 2.77 3.02 3.12 3.40 3.43 3.72 4.02 4.28 4.64 5.03 5.20 5.51 5.62 6.31 6.54 6.61 6.71 7.24
35 × 37 f¢
0.12
0.54 2.70 0.54 2.94 5.79 0.81 3.21 0.42 0.57 0.39 0.03 0.99
E (eV) 2.29 2.33 2.34 2.65 2.76 3.01 3.11 3.36 3.38 3.70 4.00 4.26 4.59 4.97 5.49 5.57 6.27 6.50 6.56 6.69 6.73 6.83 7.21
f°
and 790 × 10- 24 cm 3, respectively. It is known that A/~ values as large as 10 Debye correspond to charge-transfer states where the distance between the charges is that of two neighbouring C~o molecule centres. This means that the exciton at 2.45 eV has a strong charge-transfer character and that the bound electron-hole pair is delocalized on two neighbouring molecules. By assuming that the low edge of the conduction band is at a slightly higher energy than the delocalized charge-transfer states we derive that free carriers are generated when exciting with 0.6 eV energy in excess with respect to the optical gap.
Acknowledgements 0.12
0.63 2.46 0.75 4.83 0.90 1.35 0.24 0.48 0.17 0.09 0.03 0.03 0.84
The result of the fitting is reported in Fig. 5, showing that all the main spectral features of the electroabsorption spectrum are reproduced. The calculated parameters A/x and A c~ for the electronic transition located at 2.45 eV ( 19 760 cm - 1) are 11.3 Debye
This paper contains work which has been done in collaboration with C. Taliani, R. Zamboni, H. Schlaich, J. Feldmann and L.M. Blinov. The skillful technical assitance ofP. Mei is greatfutly acknowledged, as well as financial support by the European Community Basic Research Action Esprit 8013LEDFOS Project.
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