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In a film with large dielectric constant $\kappa$ the electric field of anelectron spreads inside the film before exiting the film at large distances oforder of $\kappa d$ ($d$ is the film width). This leads to the logarithmicCoulomb repulsion between electrons and modifies the shape of the Coulomb gapin the density of localized states in a doped film. As a result the variablerange hopping conductivity in such a film has a peculiar temperaturedependence, where the domain of the $\ln \sigma (T) \propto (T_0/T)^{p}$dependence, with the index $p \simeq 0.7$, is sandwiched between the twodomains with $p = 1/2$.

Variable range hopping in thin film with large dielectric constant