A model for the dynamics and internal structure of planar doping fronts   in organic semiconductors
  The dynamics and internal structure of doping fronts in organic semiconductors are investigated theoretically 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. Closed expressions for the front velocities and the ion concentrations in the doped regions are obtained. The analytical theory is employed to describe the acceleration of the p- and n-fronts towards each other. The analytical results show very good agreement with the experimental data. Furthermore, it is shown that the internal structure of the doping fronts is determined by 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 predictions 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. 
M. Modestov, V. Bychkov, D. Valiev, M. Marklund
cond-mat.mtrl-sci