Scaling theory of localization and non-ohmic effects in two dimensions

Abstract

A scaling argument for the conductance G of a disordered electronic system permits interpolation for the behavior of G between the localized and extended limits. For dimensionality d>2, there is a mobility edge at which the conductivity goes continuously to zero. At d=2, there is no true metallic conduction; the conductivity goes smoothly from logarithmic to exponential decrease with sample size L. A perturbation calculation confirms the ℓn L behavior for weak disorder. At finite temperature T and electric field E, effective length scales depending upon T and E are derived on the basis of relaxation and heating models for purposes of comparison with experiments on thin films. These show non-ohmic ℓn T and ℓn E contributions to the conductivity.