Bipolaron energy levels

However, when exceeds said critical valne a significant interface dipole can be formed. Positive charges are transferred from the metal to the semiconductor and the position of the Fermi level at the interface becomes pinned at an energy level interpreted as the hole polaron/bipolaron energy level in the polymer semiconductor. This simple picture suggests that, at least in the case of solntion-deposited polymers on common hole-injecting contacts, chemical interactions between the metal and... 

Fig. 4. Energy level diagrams showing possible electronic configurations for positively-charged polaron (a) and bipolaron (b) defects and (c) a schematic bipolaron band model. The negatively-charged polaron would carry three electrons and the bipolaron four. Also shown is the neutral polaron-exciton (d) which would decay to restore the chain structure.

Fig. 5.6. Sketch of the energy levels of free holes and bipolarons in ordered and disordered areas of a polymer film.

If two polarons of like sign are formed close to each other, a bipolaron is formed. Two energy levels are created by a bipolaron in the bandgap. They are both occupied either by two electrons (for a negative bipolaron) or by two holes, i.e. they are empty (in the case of a positive bipolaron). The bipolaron has no spin. The bipolaron may not be stable because of the repulsion of the two polarons which constitute the bipolaron. However the dopant ions in the neighborhood stabilize the bipolaron. 

Optical Signatures of Solitons, Polarons, and Bipolarons The formation of these excitations generates energy levels corresponding to optical transitions below the fundamental absorption that between the valence and the conduction band in one-electron models (but see Section... 

Because CPs conduct current without having a partially empty or partially filled band, concepts from solid state physics are used to explain the electronic phenomenon in these polymers. Thus, chemists refer to solitons, polarons, and bipolarons when they discuss the fundamentals of CPs. And, Fig. 1 shows the energy level diagram for an undoped, slightly doped, and heavily doped polymer to further illustrate the concept of doping. 

Figure 7.1 Schematic energy levels of singlet, triplet, trapped polaron, and bipolaron manifolds, and free carriers in luminescent n-conjugated polymers.

Note however, that Equation 19.12a holds only in the absence of charging of surface states, dopants, bipolarons or polarons, which can alter the interfacial energy level alignment and ultimately the value of V Bi- In the more general case, dipoles need to be included and 19.12a becomes ... 

FIGURE 21.15 Schematic drawing of the energy level alignment at interfaces of PFO and different metallic substrates. In all cases, the Fermi level of the substrate ( p) is situated between the negative and positive bipolaron levels. 

FIGURE 22.3 Energy levels and associated optical transitions of positive polaron and bipolaron excitations. The full and dashed arrows represent allowed and forbidden optical transitions, respectively. H, S, and L are HOMO, SUMO, and LUMO levels, respectively, and u and g are odd and even parity representations, respectively. 2too(P) and 2o)o(BP) are assigned. (From Vardeny, Z.V. and Wei, X., Handbook of conducting polymers, 2nd ed., eds. T.A. Skotheim, R.L. Elsenbaumer, and ]. Reynolds, Marcel Dekker, New York, 1998. With permission.)... 

Figure 3.6 Scheme of energy level of negative an extra electron, (c) Bipolaron state formed polaron and bipolaron in conjugated polymers upon the addition of a second electron, which after full relaxation of the polymer structure (the corresponds to the combination of two self-localized states), (a) A neutral polymer. polarons. 

Chemical or electrochemical doping (oxidation and incorporation of counterions) results in the generation of a polaron level at midgap. Further oxidation leads to the formation of bipolaron energy bands in... 

In Eq. (1), C is a representative conductive polymer containing cationic radicals stabilized over x units, and A is the counterion that is used to maintain charge neutrality. The formation of radical cations as a result of doping can lead to charge defects giving rise to polaron or bipolaron (bivalent cation for a two-electron loss) energy levels responsible for conduction [75,76]. 

Next, we discuss the electronic transitions due to polarons, bipolarons, and soli-tons in a polymer chain on the basis of a theoretical study reported by Fesser et al. [48] on a continuum electron-phonon-coupled model. The electronic energy levels of a neutral infinite polymer and those of polarons, bipolarons, and solitons are shown schematically in Figure 4-5. 

Figure 4-16. Schematic structures of polythiophene chains doped with electron acceptors (dopant content, 25 mole% per thiophene ring) and bonding electronic levels of positive polarons and bipolarons. la) Polaron lattice (b) bipolaron lattice. A. acceptor +. positive charge negative charge , electron —, electronic energy level.

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