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"Theoretical calculations give 1.0 eV [13.105] and 0.8 eV [13.145]. Theoretical calculations give (1.9, 2.7) eV [13.105] and (2.4, 2.4) eV [13.145], CEELS measurements yield 1.3 eV [13.101]. dEELS measurements yield 2.75 eV [13.101],

"Theoretical calculations give 1.0 eV [13.105] and 0.8 eV [13.145]. Theoretical calculations give (1.9, 2.7) eV [13.105] and (2.4, 2.4) eV [13.145], CEELS measurements yield 1.3 eV [13.101]. dEELS measurements yield 2.75 eV [13.101],

60 and that these compounds are therefore strongly ionic. This conclusion is in agreement with that reached theoretically by Erwin and Pederson [13.145], who calculated only a 4% admixture of K and C60 states in the electronic band structure of K^C^. The insensitivity of the optical data in Fig. 13.26 to the particular dopant also rules out the assignment of any of the spectral features to charge transfer excitations between C®0 - and M-derived states or to transitions between filled and empty alkali metal states. All the structure in the e2((o) data is therefore identified with dipole transitions between states associated with the C60 hexanion

Although it has not yet been well established that M^Q,, solids can be described as ordinary band solids, a comparison between energy band theory for K^Qq [13.105,145] and the experimental data can be made. Such a comparison is useful for identifying the interband transitions responsible for the peaks in the e2(«j) spectrum. The thin solid curve in Fig. 13.26 (right-hand scale) represents theoretical LDA calculations for the interband contribution to e2(o>) by Xu et al. [13.105]. The theoretical e2(w) is based on an electronic band structure calculation similar to that reported by Erwin and Petersen and includes the effects of the p • A matrix elements for the k points throughout the Brillouin zone. In agreement with theoretical calculations [13.105], the data in the figure show that the M6C60 compounds exhibit a series of distinguishable peaks in e2(w) on the order of ~1 eV in width. It is, however, seen that the positions of the experimentally determined absorption bands are consistently upshifted by ~0.5 eV relative to the theoretical peak positions. Nevertheless, the shape of the theoretical e2(w) spectral features reflects well that obtained by experiment, although the magnitude of the calculated e2(w) (right-hand scale) is somewhat higher than the experimental e2(w) (left-hand scale) in Fig. 13.26.

To assign peaks within the simple band picture in the low energy e2(w) data to particular band-to-band transitions, e2(a>) peak frequencies are compared to the energy difference between the centers of a particular valence band (Vf) and conduction band (C,). For M6C60 the major contributions to e2(a>) come from the following bands: V, = tXu, V2 = hu, Cx = tXg and C2 = t2u, hg [13.77], in accordance with band structure calculations [13.105,145]. Consistent with this notation, the four lowest energy features in the e2(w) curve for M6C60 are identified with the transitions Vx -»• Cx (1.1 eV), Vx C2 (2.4 eV), V2 Cx (2.8 eV), and V2 -> C2 (3.85 eV), essentially independent of M, as summarized in Table 13.6. The t2u- and /tK-derived bands in M6C60 are too close together in energy to give rise to separate peaks in e2(co) and therefore are considered to be quasidegener-ate. Of the two possible groups of transitions in Vx C2, higher oscillator strength is expected for the -> hg transitions, unless solid-state interactions and/or vibronic coupling are particularly effective in activating the tXu -» t2u transitions. Furthermore, both the Vx ->• C2 and V2 -> Cx, transitions lie too close in energy and are not separately resolved in the e2((o) spectrum of Fig. 13.26. Finally, the Lorentz oscillators introduced to describe the optical reflection and transmission of the M6C60 compounds above 4.5 eV (see Table 13.6 and Fig. 13.26) are not associated with any sharp spectral features in the optical spectra, but rather were introduced to simulate the broad absorption between 3.5 eV and 6.0 eV in the 91 and ST spectra. No attempts were made to compare the positions of this broad absorption with theory [13.77].

Using in situ K doping of C60 films on transparent substrates, optical absorption of K^Q,, films has been recorded as a function of exposure to K vapor [13.96-99], Simultaneous optical and electrical resistivity measurements were made in the vacuum chamber in which the C^q films were doped, and the evolution of the optical transmission and electrical resistivity from K exposure were recorded. On the basis of the observed optical spectra it was concluded [13.98] that for 0 < x < 3, the K^Cgg system exhibits mixed phase behavior. Specifically, it was shown that in the region 300-800 nm, the optical density of the K-doped film could be fit first as a linear combination of C60 and K3C60 spectra until the resistivity reached a minimum, signaling the formation of the pure metallic K3Q0 phase. Further exposure to K beyond the K3C60 stoichiometry re-

suited in a spectrum well fit by a linear combination of the spectra for K3C60 and K^Qq. The optical transmission spectra for the semiconducting Kf)C60 phase were analyzed in some detail and the peaks in the optical density were identified with specific interband transitions by noting the structures which were inhanced in intensity upon doping with K (i.e., transitions from the tXu band) and those that were suppressed or quenched (such as hu tu and the hg + gg —>• tlu transitions). The results for interband transitions of three in situ optical studies of K^C^ as a function of alkali metal doping are summarized in Table 13.7 [13.96-99]. Also included in Table 13.7 for comparison are the interband transitions given in Table 13.6 for Kf)C60 [13.77], as obtained from the e(co) analysis discussed above. While overall agreement between the experimental results from the four groups of investigators is excellent, the identification of the interband transitions in some cases remains tentative. Good agreement is also achieved between the optical data summarized in Table 13.7 and EELS data for

In the above discussion the optical spectra were considered in terms of a simple band picture. An alternative discussion of the optical spectra for N^Qo can be made in terms of excitons, which emphasize the importance of the electron-hole interaction in the optically excited state. Harigaya and Abe [13.148] have considered molecular excitons in the M6C60 compounds using the same model they used for solid C60 (see §13.3.2). As for the case of pristine C60, bond disorder is used to simulate lattice fluctuation effects in the M6C60 compounds. Their model calculation was carried out in the Hartree-Fock approximation using a single excitation configuration interaction, and the excitons were localized on a single anion as Frenkel-

Table 13.7

Energies (eV) of the electronic transitions in thin films of pristine K^C^ as identified from optical transmission studies.

Transitions

Transition energies (eV)

aRef. [13.96], ftRef. [13.97], cRef. [13.98], dRef. [13.77,146],

Fig. 13.27. Calculated optical absorption spectra for C^,, shown in arbitrary units, (thick line) [13.148], and compared with experimental optical data for K^C^ are taken from Pichler et al. [13.97] (thin line), and with experimental EELS data for RbjQ, from Sohmen and Fink [13.101] (dots).

Energy (eV)

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