Equilibrium theory of space charge layers in conjugated polymers II. The transition to high densities

For conjugated polymers whose charged excitations are electron and hole pol arons (P) and bipolarons (BP) we presented in part I a non-degenerate equil ibrium description for space charge layers occurring in devices. In this pa per a description is given which considers the BP lattice formation at high densities including the transition between both limits which is important at finite temperatures. The theory is based on a novel approximation for th e potential and temperature dependence of the P and BP densities which make s use of the degenerate limit. The latter is treated separately first for t he soliton lattice. The puzzle of a high surface electric field at low band bending and a divergency for the differential capacitance are clarified. N umerical ground state energy calculations for long chains yield the depende nces of the BP and P formation energies on the density. The results can be described analytically with high accuracy in terms of the (mon simple) func tional dependence of the soliton lattice. The formation energies used in th e new approximation must be slightly modified to account for the deviation from the ground state at finite temperatures. Surface electric field and ca pacitance are calculated and discussed. Both are still extreme large in acc umulation (and inversion). Although the divergency of the capacitance disap pears there remains a large maximum indicating an extremely small extension of the accumulation layer almost at the limit of the theoretical model bas ed on the use of a macropotential. (C) 1999 Elsevier Science S.A. All right s reserved.