Hopping conductivity in granular metals near the insulator–metal transition

Percolation theory of activated hopping conductivity on metal grains embedded in a dielectric matrix has been developed. The Coulomb gap, reduced by screening, has been shown to close at the percolation threshold. The Hall constant has been estimated assuming greater mobility of holes compared to that of electrons due to smaller variation in the ionization potential of grains than in the electron affinity. The electric conductivity has been calculated as a function of the volume fraction of metal and the temperature. A few factors including localization of electrons in the Coulomb potential wells and multiple ionization of grains have been found responsible of the temperature dependence usually referred to as the variable range hopping.