THEORY OF DIFFUSION AND ELECTRIC CONDUCTION DUE TO QUANTUM TUNNELING ALONG THE C-AXIS OF LAYERED MATERIALS

Abstract

A lattice-kinetic theory is developed for the transport phenomena arising from the electron tunneling along the c-axis of a layered material such as wurtzite and graphite. The electron is allowed to tunnel through the potential barrier between the conducting layers with the success rate equal to the quantum transmission coefficient t if and only if it was proceeding toward the barrier before each transmission attempt. Each attempt is assumed to occur at a random time and without coherence. Under these conditions, the diffusion coefficient D is given by D = alpha-2/2<tau>t/1-t where alpha is the separation between the layers and <tau> is the average time between successive attempts. The above formula is in agreement with the macroscopic Landauer formula [Phil. Mag. 21, 863 (1970), equation (1)] but all relevant quantities (alpha, t, <tau>) are now defined microscopically. An explanation for the observed strong anisotropy in the conductivities along, and perpendicular to, the c-axis is proposed in terms of the charge states of conducting layers.