The last process contributing to the molecular picture of the space-charge field formation is the recombination of a free hole with an ionized acceptor. The theoretical approach most commonly used to describe this process is the Langevin treatment,M. Pope and C. E. Swenberg, "Electronic processes in organic crystals and polymers"(Oxford University Press, New York, 1999). which treats recombination as a random process, assuming that the carriers are produced statistically independent of each other and that the mean free path (l) of the carriers is less than the Coulomb radius of capture (rc) of one carrier by a counterion of the opposite sign (e.g. ionized acceptor ):
where e is the charge of the electron, ε0 is the dielectric permittivity of vacuum, ε is the dielectric constant, kB is the Boltzmann constant, and T is the temperature.
In the Langevin model, recombination rate γ is proportional to charge carrier mobility μ (and therefore, is electric field-dependent):
