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. \textcopyright{} 1996 The American Physical Society.