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 ${\mathit{T}}_{\mathrm{eff}}$(T,E) which in the limit of eEa≫${\mathit{k}}_{\mathit{B}}$T is close to 0.67eEa/${\mathit{k}}_{\mathit{B}}$. The conductivity σ(T,E) collapses to a single universal curve when plotted as a function of the effective temperature ${\mathit{T}}_{\mathrm{eff}}$(T,E). This confirms the fact that ${\mathit{T}}_{\mathrm{eff}}$ determines the conductivity. The same effective temperature also determines the dependencies of the steady state and transient photoconductivities on T and E.