Conduction by Small Polarons in Large Electric Fields

The bandwidth of small polarons at low temperatures is so narrow [∼ ${10}^{-3\mathrm{}}$ (optical phonon energy)] that an electric field of the order of ${10}^3$V/cm produces a potential difference between neighboring atoms that is comparable with the bandwidth. It is shown that the electron states are then localized and that charge transport proceeds by hopping from site to site, the conductivity being much less than the low-field conductivity by nonlocal electrons. The field-induced transition from band to hopping modes of transport is marked by a region of constant current or negative resistance; at higher fields conduction remains Ohmic until fields of the order of ${10}^6$V/cm are reached.