Temperature and electric-field dependence of hopping transport in low-dimensional devices.

Abstract

A theoretical calculation has been performed for the variable-range-hopping (VRH) conduction mechanism in the presence of temperature and electric field for quasi-two-dimensional (QTD) and quasi-one-dimensional (QOD) systems. In the present calculation, it is assumed that the localized states are randomly distributed both in energy and space coordinates. The states both below and above the Fermi level are included in the calculation of the hopping range and conductivity. The present approach differs significantly from the percolation method and others in the calculation of the mobility and the conductivity. The expressions for the hopping range, the mobility, and the conductivity are obtained for the constant and the energy-dependent density of states. The expression of the conductivity for the constant density of states can be reduced to that of Mott in certain approximations. The effect of electron-electron interaction in the calculation of the conductivity and hopping range has been included through the density of states. After some approximations, the present expression of the conductivity can be reduced to that of Efros and Shklovskii. The logarithm of the conductivity follows the (1-${\mathrm{\ensuremath{\beta}}}^{2}$${)}^{3/8}$ and \ensuremath{\surd}1-${\mathrm{\ensuremath{\beta}}}^{2}$ electric-field dependence for QTD and QOD systems, respectively, in the presence of the electron-electron interaction and a weak electric field. Here \ensuremath{\beta} is directly proportional to an electric field. The present calculations are applied to explain the recent conductivity experiments on ${\mathrm{PrBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathit{y}}$ (PBCO) films. A possible crossover from Mott-type VRH to Efros-and-Shklovskii-type VRH has been observed in PBCO.