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 polarons (P) and bipolarons (BP) we presented in part I a non-degenerate equilibrium description for space charge layers occurring in devices. In this paper 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 the potential and temperature dependence of the P and BP densities which makes use of the degenerate limit. The latter is treated separately first for the soliton lattice. The puzzle of a high surface electric field at low band bending and a divergency for the differential capacitance are clarified. Numerical ground state energy calculations for long chains yield the dependences of the BP and P formation energies on the density. The results can be described analytically with high accuracy in terms of the (more simple) functional dependence of the soliton lattice. The formation energies used in the new approximation must be slightly modified to account for the deviation from the ground state at finite temperatures. Surface electric field and capacitance are calculated and discussed. Both are still extreme large in accumulation (and inversion). Although the divergency of the capacitance disappears there remains a large maximum indicating an extremely small extension of the accumulation layer almost at the limit of the theoretical model based on the use of a macropotential.