Electronic Transition and Band Gap

The incorporation of siloles in polymers is of interest and importance in chemistry and functionalities. Some optoelectronic properties, impossible to obtain in silole small molecules, may be realized with silole-containing polymers (SCPs). The first synthesis of SCPs was reported in 1992.21 Since then, different types of SCPs, such as main chain type 7r-conjugated SCPs catenated through the aromatic carbon of a silole, main chain type cr-conjugated SCPs catenated through the silicon atom of a silole, SCPs with silole pendants, and hyperbranched or dendritic SCPs (Fig. 2), have been synthesized.10 In this chapter, the functionalities of SCPs, such as band gap, photoluminescence, electroluminescence, bulk-heterojunction solar cells, field effect transistors, aggregation-induced emission, chemosensors, conductivity, and optical limiting, are summarized. 

Polydibenzosiloles are wide band gap SCPs. Poly(3,6-dibenzosilole)s 5 (Fig. 3) show absorptions peaks (Aab) at 283 nm and absorption edges at 310 nm in solutions as well as in thin films.22 The calculated optical band gaps of poly(3,6-dibenzosilole)s are 4.0 eV, which is the widest band gap so far 

Poly(2,5-silole) 7 shows a Aab of 482 nm at room temperature.24 A band gap of the polymer, if calculated with the absorption edge (650 nm), is 1.9 eV. A silole-thiophene alternating copolymer 8 can show a further decreased band gap.25 The copolymer displays a broad absorption spectrum with Aab at 648 nm in chloroform. The calculated band gap from the absorption edge is only 1.55 eV, a very small value so far reported for the synthesized SCPs. 

Other SCPs, including many types of copolymers, possess band gaps between 4.0 and 1.55 eV. The largely varied electron transitions and band gaps of SCPs imply that the optoelectronic properties of SCPs could be tuned. 

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Semiconductors can be divided into two groups direct and indirect band gap materials. In direct semiconductors the minimum energy in the conduction band and the maximum in the valence band occur for the same value of the electron momentum. This is not the case in indirect materials. The difference has profound consequences for the transitions of electrons across the band gap in which light is emitted, the radiative transitions, of interest here. 

The KS orbital energies can also be used for qualitative interpretation of the electronic spectra of atoms and molecules " and band gaps in solids.In the HF or semiempirical ZDO methods, the unoccupied MOs are subject to the self-consistent field of all N electrons, whereas the occupied MOs are subject to the self-consistent field of the N - 1) electrons (an electron in an occupied orbital does not interact with itself). So, for unoccupied orbitals of the N-electron system, the MO energy Sa corresponds to the interactions of an extra N + l)th electron. For the excitation of an electron from the occupied MO to the unoccupied MO an electron in electron affinity, namely with , . As a result, the MO energy differences, Ea — Si, obtained from HF or semiempirical INDO/S calculations are not estimates of transition energies, they have to be combined with appropriate Jand Kintegrals (see Chapter 2.38). 

Optical absorption measurements give band-gap data for cubic sihcon carbide as 2.2 eV and for the a-form as 2.86 eV at 300 K (55). In the region of low absorption coefficients, optical transitions are indirect whereas direct transitions predominate for quantum energies above 6 eV. The electron affinity is about 4 eV. The electronic bonding in sihcon carbide is considered to be predominantiy covalent in nature, but with some ionic character (55). In a Raman scattering study of vahey-orbit transitions in 6H-sihcon carbide, three electron transitions were observed, one for each of the inequivalent nitrogen donor sites in the sihcon carbide lattice (56). The donor ionization energy for the three sites had values of 0.105, 0.140, and 0.143 eV (57). 

Color from Color Centers. This mechanism is best approached from band theory, although ligand field theory can also be used. Consider a vacancy, for example a missing CF ion in a KCl crystal produced by irradiation, designated an F-center. An electron can become trapped at the vacancy and this forms a trapped energy level system inside the band gap just as in Figure 18. The electron can produce color by being excited into an absorption band such as the E transition, which is 2.2 eV in KCl and leads to a violet color. In the alkaU haUdes E, = 0.257/where E is in and dis the... 

Calculations for Ceo in the LDA approximation [62, 60] yield a narrow band (- 0.4 0.6 eV bandwidth) solid, with a HOMO-LUMO-derived direct band gap of - 1.5 eV at the X point of the fee Brillouin zone. The narrow energy bands and the molecular nature of the electronic structure of fullerenes are indicative of a highly correlated electron system. Since the HOMO and LUMO levels both have the same odd parity, electric dipole transitions between these levels are symmetry forbidden in the free Ceo moleeule. In the crystalline solid, transitions between the direct bandgap states at the T and X points in the cubic Brillouin zone arc also forbidden, but are allowed at the lower symmetry points in the Brillouin zone. The allowed electric dipole... 

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