Equilibrium theory of space charge layers in conjugated polymers I. Non-degenerate limit

Abstract

For conjugated polymers whose charged excitations are electron and hole polarons (Ps) and bipolarons (BPs) we present an equilibrium description for space charge layers occurring in devices such as organic light-emitting diodes or organic field-effect transistors. In this paper a general description for the non-degenerate case is developed. The theory is concentrated upon the device related quantities: densities, band bending (surface potential) and its connection with the surface electric field and hence with the total charge in the layer, differential capacity, and characteristic lengths for depletion, accumulation and inversion. In comparison with usual inorganic semiconductors special attention is devoted to the limit of non-degeneration and to general limits which arise from using a macropotential which should be sufficiently smooth in space compared with the extension of the charged states forming the space charge layer. A further limit is connected with the maximum electric field set, e.g., by breakthrough. The lower formation energy of the Ps or BPs acts similarly to the band edge in usual semiconductors and, instead of the effective densities of states (of the order 10 19 cm −3), one has essentially to use the density of monomer units (10 21–10 22 cm −3). If BPs are energetically favored, with dependence on doping and temperature in the bulk, either Ps or BPs dominate; in strong accumulation or inversion the BPs become the dominant carriers. Since the BPs are doubly charged one has then a stronger screening and extremely thin accumulation or inversion layers approaching the limits of such a treatment.