A derivation for the steady‐state currentJproduced by a large homogeneous electric fieldE0in the presence of a concentration gradient is presented which includes explicitly the effects due to lattice discreteness. The resulting equation isJ=4a&ngr;exp(−W/kBT)sinh(ZeE0a/kBT)[C(L)−C(0)exp(ZeE0L/kBT)]/[1−exp(ZeE0L/kBT)],whereC(0) andC(L) are the boundary concentrations of the diffusing species at the interfaces of the planar film at positionsx=0 andx=L;e, the electronic‐charge magnitude;Ze, the charge per particle of the diffusing species; 2a, the distance between adjacent potential minima;v, the frequency at which the ion attempts energy barriers which have heightWin zero field;kB, the Boltzmann constant; andT, the absolute temperature. A derivation valid in the limit of a continuum model is also presented, and the results are compared numerically. The equations for the discrete and continuum models reduce to the results predicted by the ordinary linear diffusion equation for electric fields below approximately 105V/cm. The relevance of the equations to the phenomena of anodic and thermal oxidation and to thin‐film current‐voltage devices is briefly described.