  Electron transport in electric-field-driven tight-binding lattice coupled to
fermion baths is comprehensively studied. We reformulate the problem by using
the scattering state method within the Coulomb gauge. Calculations show that
the formulation justifies direct access to the steady-state bypassing the
time-transient calculations, which then makes the steady-state methods
developed for quantum dot theories applicable to lattice models. We show that
the effective temperature of the hot-electron induced by a DC electric field
behaves as $T_{\rm eff}=C\gamma(\Omega/\Gamma)$ with a numerical constant $C$,
tight-binding parameter $\gamma$, the Bloch oscillation frequency $\Omega$ and
the damping parameter $\Gamma$. In the small damping limit $\Gamma/\Omega\to
0$, the steady-state has a singular property with the electron becoming
extremely hot in an analogy to the short-circuit effect. This leads to the
conclusion that the dissipation mechanism cannot be considered as an implicit
process, as treated in equilibrium theories. Finally, using the energy flux
relation, we derive a steady-state current for interacting models where only
on-site Green's functions are necessary.
