Current-field and conductivity-field characteristics of thin layers: the predictions of the Bottger-Bryksin model

Phonon-assisted hopping of electrons between spatially distinct locations is one of the basic transport mechanisms in solids. In the present contribution compare the current-field, and differential conductivity-field characteristics, calculated within the Bottger-Bryksin model applied to thin layers with spatially nonuniform distributions S(x) of hopping centers. In particular, we consider exponential and bi-exponential spatial distributions of centers, i.e. S(x) ∝ exp(-x/D), and S(x) -∝[exp(-x/D) + exp(-(L x)/D)], where L is the layer thickness, and D the distribution parameter. Although the model allows the calculations for both on-diagonal (energetic) and off-diagonal (positional) disorder, here we discuss only the case of discrete energy level of hopping centers. We show that the Bottger-Bryksin model predicts a strong ´tapping´ effect in the case, where the surface densities of hopping centers at both contacts differ significantly. In such cases wide field intervals of negative differential conductivity are expected