Study of the negative resistance phenomenon in transition metal oxide films from a statistical mechanics point of view

The mechanism of the differential negative resistance behavior observable in transition metal oxides such as Ti O2, NiO, and Nb2 O5 is theoretically developed in terms of the order to disorder transition of local conducting pathways, so called filaments, by applying statistical mechanics. Joule heat is taken as a heat source giving rise to an increase of temperature in the filaments. The free energy of the filaments is evaluated by taking the site percolation model as well as the nonhomogeneity of an order parameter into account. It is concluded that the transition of a filament from the conducting state, which is dominated by the internal bonding energy term, to the nonconducting state is due to an increased contribution of the entropy term to the system's total energy at a higher temperature. The calculation results also show that the rupture of a filament occurs in the middle of the filament when the filaments are in contact with thermally conducting metal electrodes, such as Pt.