By using the steady-state density matrix at an infinite time after the turn-on of a high electric field, in the presence of arbitrary phonon and impurity scattering, the longitudinal DC current is investigated for arbitrary temperatures. The current is carried by a hopping process between different sites with the aid of some scattering mechanisms. If polar optical-phonon scattering is assumed, the current versus field characteristics exhibit stair-like rises at F=h(cross) omega 0/aen associated with the onset of the nth hopping process for which the hopping distance is na (a lattice constant; n=1,2,3,...). As for the current component due to the nth hopping process, it is demonstrated that for the lower-field region F<or=h(cross) omega 0/aen, the current is proportional to F-1exp((naeF-h(cross) omega 0)/kBT) while for higher field region F>h(cross) omega 0/aen, it is essentially independent of temperature but inversely proportional to the electric field.