Variable range hopping in thin film with large dielectric constant

TL;DR

This paper investigates how a large dielectric constant in thin films affects electron interactions and conductivity, revealing a unique temperature dependence in variable range hopping due to modified Coulomb interactions.

Contribution

It introduces a new understanding of Coulomb gap modification and variable range hopping behavior in films with large dielectric constants.

Findings

Logarithmic Coulomb repulsion modifies the density of states.

Temperature dependence of conductivity shows a new intermediate regime.

The exponent p in conductivity varies between 1/2 and approximately 0.7.

Abstract

In a film with large dielectric constant $\kappa$ the electric field of an electron spreads inside the film before exiting the film at large distances of order of $\kappa d$ ($d$ 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 $\ln \sigma (T) \propto (T_0/T)^{p}$ dependence, with the index $p \simeq 0.7$, is sandwiched between the two domains with $p = 1/2$.