Hopping conduction in strong electric fields: Negative differential   conductivity
  Effects of strong electric fields on hopping conductivity are studied theoretically. Monte-Carlo computer simulations show that the analytical theory of Nguyen and Shklovskii [Solid State Commun. 38, 99 (1981)] provides an accurate description of hopping transport in the limit of very high electric fields and low concentrations of charge carriers as compared to the concentration of localization sites and also at the relative concentration of carriers equal to 0.5. At intermediate concentrations of carriers between 0.1 and 0.5 computer simulations evidence essential deviations from the results of the existing analytical theories.   The theory of Nguyen and Shklovskii also predicts a negative differential hopping conductivity at high electric fields. Our numerical calculations confirm this prediction qualitatively. However the field dependence of the drift velocity of charge carriers obtained numerically differs essentially from the one predicted so far. Analytical theory is further developed so that its agreement with numerical results is essentially improved. 
A. V. Nenashev, F. Jansson, S. D. Baranovskii, R. \"Osterbacka, A. V.   Dvurechenskii, F. Gebhard