Correlation effects in hopping conduction: Hopping as a multi-electron transition

Abstract

The treatment of hopping between localized states as a one electron transition breaks down at high densities. We have treated the problem in terms of a correlated two electron (one phonon) transition. We neglect exchange effects. The correlation effect consists of the movement of two (or more) electrons simultaneously whenever it lowers the energy difference between initial and final state of the system. This is seen to lower the activation energy over the one electron process, an effect noticeable at low temperatures, moderate densities, and moderate compensation in impurity conduction. The onset of the effect is seen to occur at a density on the order of $\text{(}\text{3}\text{4}\text{π) (e}{}^2\text{a/2kTK)−}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ for a temperature T, where K is the dielectric constant of the host medium and a is the Bohr radius of an impurity state.