Hopping Conductivity in Granular Metals

We present evidence that in granular metals the observed temperature dependence of the low-field conductivity, exp (-b{T^}) with =12, can be ascribed to a relationship sE₂=const between s, the separation of neighboring metal grains, and E₂, the electrostatic energy required to create a positive-negative charged pair of grains. This relationship results from simple considerations of the structure of granular metals. The predictions of the theory, for both the high- and the low-field electrical conductivity, are in excellent accord with experimental results in granular Ni-SiO₂ films.