Internal Structure of Planar Electrochemical Doping Fronts in Organic Semiconductors

Abstract

The internal structure of electrochemical doping fronts in organic semiconductors is investigated using an extended drift-diffusion model for ions, electrons, and holes. The model also involves the injection barriers for electrons and holes in the partially doped regions in the form of the Nernst equation, together with a strong dependence of the electron and hole mobility on concentrations. It is shown that the internal structure of the doping fronts is controlled by a balance between the diffusion and mobility processes. The asymptotic behavior of the concentrations and the electric field is studied analytically inside the doping fronts. The numerical solution for the front structure confirms the most important findings of the analytical theory: a sharp head of the front in the undoped region, a smooth relaxation tail in the doped region, and a plateau at the critical point of transition from doped to undoped regions. The theoretically predicted complex structure of the doping fronts is in agreement with the previous experimental data. The acceleration of the p- and n-fronts toward each other in light-emitting electrochemical cells is described. The theoretical predictions for the planar front acceleration are in a good quantitative agreement with the experimental measurements for the backside of the curved doping fronts.