Effective temperature of hopping electrons in a strong electric field

We study numerically the energy distribution of electrons and the hopping conductivity as a function of the temperature T and electric field E in the tail of the density of states of an amorphous semiconductor where states are localized with a localization length a. We find a Boltzmann distribution with an effective temperature Teff(T,E) which in the limit of eEa{}kBT is close to 0.67eEa/kB. The conductivity {σ}(T,E) collapses to a single universal curve when plotted as a function of the effective temperature Teff(T,E). This confirms the fact that Teff determines the conductivity. The same effective temperature also determines the dependencies of the steady state and transient photoconductivities on T and E.