Bipolaron lattice formation at metal-polymer interfaces

Abstract

We describe a model for metal-polymer interfaces based on the nondegenerate continuum model of Brazovskii and Kirova for the electronic properties of polymers. The correct analytic equations for a bipolaron lattice in this model are stated and the electronic properties of the bulk polymer, i.e., the energy-level structure, the energy density, and the chemical potential as a function of electron density are obtained numerically. We find that the bipolaron lattice is unstable at high densities when the intrinsic gap parameter exceeds a critical fraction of the total energy gap. The electronic properties of the bulk polymer are used for modeling the metal-polymer interface. The charge density near a metal-polymer interface is found from the electrostatic potential and an analytic expression for the bipolaron chemical potential assuming that the contact is in equilibrium with the polymer layer. Poisson's equation is integrated to determine the electrostatic potential. We find that a large charge density is transferred into the polymer layer if the Fermi level of the metal contact is higher than the negative bipolaron formation energy per particle or lower than the positive bipolaron formation energy per particle. The transferred charge lies very close to the metal-polymer interface as a bipolaron lattice with charge density progressively decreasing away from the interface. The transferred charge gives rise to a region of rapid ''band bending,'' pins the Fermi level, and establishes the effective Schottky energy barrier. Upon increasing the metal Fermi level above the bipolaron formation energy per particle, the effective Schottky barrier saturates at the energy difference between the polaron formation energy and the bipolaron formation energy per particle. The model results are useful in interpreting recent measurements of internal photoemission, device electroabsorption, and capacitance-voltage characteristics in polymer light-emitting diodes.

Full phase diagram of the massive Gross–Neveu model

“…It is well known that static solutions of the GN model must correspond to reflectionless Schrödinger potentials [7,32]. The fact that the ansatz (27) leads to self-consistency as shown in Refs. [9,10] is therefore quite plausible.…”

“…Notice that the simple and intuitive relation between the single baryon and the crystal exhibited in Eq. (29) is hidden in the corresponding Dirac potentials (27) and (5) due to the non-linear relationship between S and U ± .…”

“…We first became aware of this ansatz through works on the bipolaron lattice for non-degenerate conducting polymers [21], [22], [24]- [27]. The following discussion is based on these references as well as on mathematical literature on periodic solitons [28,29].…”

Bipolaron recombination in conjugated polymers

“…[2][3][4][5] Some of the early studies concentrated on the stability of bipolaron. [6][7][8][9][10] It is now clear that both the electron-phonon coupling and the electron-electron interaction play an important role in forming bipolarons: at low concentration of carriers, carriers are more likely in the form of polarons, while at high concentration of carriers they tend to favor bipolarons. 6 Bipolarons may also coexist with polarons in conjugated polymers.…”

Spontaneous charge transfer at organic-organic homointerfaces to establish thermodynamic equilibrium

“…9 It has been suggested that the transition from vacuum level alignment to molecular orbital level pinning occurs when the HIB becomes of the same magnitude as the positive polaron relaxation energy. 9,12,13 In this case, charge must be redistributed across the interface, leading to an interface dipole. In other words, the vacuum level is changed but the hole injection barrier stays constant.…”