  Recently, it was demonstrated that electrochemical doping fronts in organic
semiconductors ex- hibit a new fundamental instability growing from
multidimensional perturbations [Phys. Rev. Lett. 107, 016103 (2011)]. In the
instability development, linear growth of tiny perturbations goes over into a
nonlinear stage of strongly distorted doping fronts. Here we develop the
nonlinear theory of the doping front instability and predict the key parameters
of a distorted doping front, such as its velocity, in close agreement with the
experimental data. We show that the instability makes the electrochemical
doping process considerably faster. We obtain the self-similar properties of
the front shape corresponding to the maximal propagation velocity, which allows
for a wide range of controlling the doping process in the experiments. The
theory developed provides the guide for optimizing the performance of organic
optoelectronic devices.
