Numerical investigation of non-ohmic hopping conduction in macroscopically non-homogeneousthin layers. Strong electron-phonon interaction

The current-field and conductivity-field characteristics of random r hopping as well as r-E hopping systems with a strong electron-phonon coupling have been calculated numerically and discussed by Bottger and co-workers (1985-86). They have assumed a random but macroscopically homogeneous distribution of centres over the sample. However, in most real cases an extremely thin layer can hardly be thought to be macroscopically homogeneous and the local hopping-centre density should depend on the distance from the electrodes. In the present work the authors apply the Bottger-Wegener procedure to random r hopping and r-E hopping systems with macroscopic average density exponentially dependent on the distance from the contact. Only a strong electron-phonon coupling will be considered, i.e. the authors shall consider small-polaron transport in a disordered solid. The influence of the inhomogeneity in the centre distribution on current field and conductivity-field characteristics may be summarized as follows. Firstly, for r-hopping transport in homogeneous layers, Bottger and Wegener observe a decrease in the differential conductivity with increasing field, its local minimum being followed by an exponential increase; the authors confirm the results for homogeneous systems, whereas for inhomogeneous systems they find that, on increasing the degree of the site distribution inhomogeneity the local conductivity minimum is no longer followed by an exponential conductivity increase, but the system becomes ohmic (conductivity saturation), at least up to the fields consistent with the assumption of constant carrier concentration. Secondly, for r-E hopping in homogeneous layers, Bottger et al. observe for not too high an energy spread in the hopping centres that the local conductivity maximum occurring just after the ohmic region is followed by a local minimum, that latter being followed by an exponential conductivity increase for still higher fields.