Hopping conduction in strong electric fields and directed percolation

Hopping conduction is considered in such strong electric fields that electron hops are mainly oriented in the direction opposite to the electric field. For half-filled and symmetrical impurity band the calculation of the hopping conductivity is reduced to the directed percolation problem on random sites, which is solved by computer simulation. For nonequal concentrations of occupied and unoccupied centers in the impurity band the hopping conductivity problem cannot be reduced to the directed percolation. In this case current is determined by trapping of electrons on those impurities which have no neighbours in rather large regions along the direction of the electron drift. As a result, their velocity is much smaller than in the case of half-filled band.