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Fig. 13.16. (a) Calculated density of electronic states for a cluster of four Cwl molecules by the Hartree-Fock approximation. The occupied (unoccupied) states are shown by the black (white) bars, (b) Density of excitations as a function of the excitation energy, showing both localized Frenkel excitons (indicated by open bars) and delocalized charge transfer-like excitons (shown as shaded bars), (c) The absorption spectrum where the Lorentzian broadening is taken as T = 0.03f (i is a scaling factor taken as 1.8 eV) [13.95], to excitons which exhibit at least a 50% probability of being delocalized over more than one molecule, while unshaded vertical bars correspond to Frenkel excitons, i.e., those that are localized primarily on one molecular site. The delocalized excitons are referred to as charge transfer (CT) excitons because the absorption of the photon to create this excited state must necessarily involve the transfer of an electron localized in the ground state on one molecule to an excited state delocalized over neighboring molecules. Similar to the calculations of Louie et al. [13.87, 111], Harigaya and Abe find that near the absorption edge, the largest oscillator strength in the spectrum lies primarily with localized (Frenkel) excitons. They therefore conclude that most of the observed photoexcited states at the absorption threshold should be identified with Frenkel-like excitons but that charge transfer excitons become important a few hundred meV above the absorption threshold.

13.3.3. Low-Frequency Dielectric Properties

Both intrinsic and extrinsic effects contribute to the low-frequency (< 1011 Hz) dielectric properties of fullerene materials, below the frequency of any intermolecular vibrations. In this low-frequency regime, the effects of oxygen and other interstitial adsorbates are particularly important.

If the interstitial sites of solid C60 are partially occupied by impurities that can transfer charge to nearby C60 molecules, then the resulting dipole moments can be significant because of the large size of fullerene molecules. Such effects have been detected by ac impedance measurements of polarization effects in M-C60-M (M = metal) trilayer structures [13.117],

Referring to Fig. 13.10, for every loss process represented by a peak in the e2(a>) spectrum, there is a rise (sometimes accompanied by a small oscillation) in e,(w), as prescribed by the Kramers-Kronig relations [13.26]. As we move below 1013Hz in frequency, e,(a)) approaches its dc value. The small difference between e,(1013Hz) % 3.9[13.77] and e,(105 Hz) % 4.4 [13.76] is perhaps due to the losses associated with the rapid rotation of the C60 molecules (at ~109Hz) at room temperature (T > 701) (see §7.1.3 and §16.1.4). From the Kramers-Kronig relations, the dc dielectric constant e,(0) can be related to e2(w) over a broad frequency range where the low-frequency e2(w) contributes most importantly to 6,(0).

Measurements of the dielectric properties of solids below ~1 MHz are usually made by placing a sample between closely spaced parallel conducting plates and monitoring the ac equivalent capacitance C(a>) and the dissipation factor D(u)) of the resulting capacitor. The capacitance is proportional to e^w), the real part of the relative dielectric function, according to the relation C(w) = ei(w)eQA/d, where A is the cross-sectional area of the capacitor, d is the separation between the plates, and e0 is the absolute permittivity of free space (8.85 x 10"12 F/m). Measurement of the dissipation factor (also known as the loss tangent) D(w) = e2(w)/e1(w) can then be used to extract the imaginary part of the dielectric function e2(w).

To avoid problems arising from changes in the plate spacing d of the C60 capacitor due to the thermal expansion of the C60 lattice, or to the structural first-order phase transition at T0l ~ 261K, or during the intercalation of oxygen or other species into the interstitial spaces of C60 solid, a microdielectrometry technique [13.118-120] has been used to measure the dielectric properties of C60 at low frequencies (from 10"2 to 105 Hz) [13.121]. Instead of using a parallel plate geometry, both electrodes in the microdielectric measurement are placed on the same surface of an integrated circuit (see Fig. 13.17), and the medium to be studied (C60 film) is

Drtvan Gate (DG)

Drtvan Gate (DG)

Fig. 13.17. (a) Schematic view of the active portion of a microdielectrometer sensor chip. CFT refers to "floating-gate charge-flow transistor," whose gate electrode (or floating gate [FG]) is one of the two interdigitated electrodes. Since the sensing electrode is electrically floating, and because of the proximity of the CFT amplifier to that electrode, a good signal-to-noise ratio can be achieved at very low frequencies (down to ~10-2 Hz), (b) Schematic cross section through the electrode region [denoted by AA' in (a)] showing the electric field pattern between the interdigitated driven gate (DG) and floating gate (FG) electrodes [13.119].

Fig. 13.17. (a) Schematic view of the active portion of a microdielectrometer sensor chip. CFT refers to "floating-gate charge-flow transistor," whose gate electrode (or floating gate [FG]) is one of the two interdigitated electrodes. Since the sensing electrode is electrically floating, and because of the proximity of the CFT amplifier to that electrode, a good signal-to-noise ratio can be achieved at very low frequencies (down to ~10-2 Hz), (b) Schematic cross section through the electrode region [denoted by AA' in (a)] showing the electric field pattern between the interdigitated driven gate (DG) and floating gate (FG) electrodes [13.119].

placed over the electrodes by thermal sublimation in vacuum [13.76]. The comb electrodes in Fig. 13.17, in contrast to parallel plates, provide a fixed calibration for both e, and e2. Such an open-face configuration also makes it possible to monitor the frequency response and dielectric properties of the C60 film dynamically as a function of doping with selected gases and other species [13.121].

A small amount of charge transfer between the oxygen and C60 molecules is responsible for creating electrical dipoles, which can be coupled by the applied ac (low-frequency) electric field. This charge transfer imposes preferential orientations of the molecules, limiting their degrees of freedom, and giving rise to dielectric loss peaks and enhanced polarization. Because of the large size of the C60 molecule, only a small amount of charge transfer is required to create a significant dipole moment, resulting in a big increase in polarization e^w) [13.121]. Broad loss peaks due to dipolar reorientations associated with interstitial hopping of oxygen impurity atoms can be thermally activated over a 0.5 eV energy barrier and a frequency prefactor of 2 x 1012 Hz. An interstitial diffusion constant for oxygen in solid C60 of ~ 4 x 10~n cm2 s 1 at 300 K has been inferred [13.121], With increasing oxygenation, the interstitial sites become nearly fully occupied, interstitial hopping is inhibited, and the loss peaks together with the enhanced polarization disappear.

13.3.4. Optical Transitions in Phototransformed C60

^ solid films can be readily transformed into a polymeric phase under irradiation with visible or ultraviolet light [13.1,122]. In this phototransformed phase, it has been proposed that C60 molecular shells are coupled together by covalent bonds to form a polymeric solid or "polyfullerene" [13.1]. Some experimental results on phototransformed Qq suggest the formation of four-membered rings located between adjacent C60 molecules through "2 + 2" cycloaddition, as discussed in §7.5 [13.2,123]. Recent theoretical calculations on the C60 dimer find that a four-membered ring is the lowest-energy configuration [13.124,125].

In this subsection we summarize results for the OA and PL spectra of phototransformed C60 solid films. The features in the PL spectra are observed to broaden and downshift by ~330 cm"1, whereas the OA features upshift and broaden considerably. These results are consistent with the reduced symmetry imposed by the introduction of covalent bonds between C60 molecules (see §7.5.1). Photopolymerization by the exciting source may also be the cause for the previously reported [13.126] problems in the spot-to-spot reproducibility in the photoluminescence spectra of C60.

In Fig. 13.18(a) we compare the room temperature absorbance \st = — log10(2") where ST is the transmission] of a C60 film (d -500 A) on a Suprasil substrate in the pristine (solid curve) and phototransformed (dashed curve) phases. In §13.3.2 and in Table 13.4 the four prominent absorption peaks in Fig. 13.18(a) at ~2.7, 3.6, 4.7, and 5.6 eV for the pristine phase are identified with predominantly "dipole-allowed" electronic transitions (see §13.1.2) [13.77].

After phototransformation of the sample, the optical bands associated with these optical transitions are noticeably broadened and reduced in peak intensity [Fig. 13.18(a)]. This broadening is attributed to a random photochemical cross-linking of C60 molecules, giving rise to inhomogeneous broadening. Cross-linking the molecular shells completely removes the degeneracies of the electronic energy levels in the C60 monomers. Also, the phototransformation generates a distribution of Qo oligomeric units. Both of these changes in the system should contribute to line broadening. It was found by fitting Lorentz oscillator functions to the absorption spectra that the width of the peak at ~3.6 eV in the "polyfullerene" phase is ~0.3 eV wider than that in the pristine phase. This ~0.3 eV broadening is consistent with the results of photoelectron spectroscopy [13.127], where the electronic energy levels (HOMO and HOMO-1 states) in the photoemission spectra

LUMO +1 LUMO

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