Variable range hopping in thin film with large dielectric constant

Abstract

In a film with large dielectric constant κ the electric field of an electron spreads inside the film before exiting the film at large distances of order of κ d ( d is the film width). This leads to the logarithmic Coulomb repulsion between electrons and modifies the shape of the Coulomb gap in the density of localized states in a doped film. As a result the variable range hopping conductivity in such a film has a peculiar temperature dependence, where the domain of the ln σ( T) ∝ (T₀/T) p dependence, with the index p ≃ 0.7, is sandwiched between the two domains with p = 1/2.