Approach in Time to Breakdown in the RRTN Model

Abstract

The phenomenon of breakdown is seen in widely different varieties of driven systems, starting from failures of mechanical systems (like fractures of materials, avalanches, (earth)-quakes) to biological systems (like denatured proteins etc.) [1]. Electrical breakdown itself can be of two different types. One is the fuse type breakdown due to the Joule heating through the ohmic conductors, and hence it is an irrerversible phenomenon. The other is dielectric breakdown. If an insulating material (made of microscopic disordered metallic and dielectric, i.e., insulating, phases) is placed between two electrodes and a voltage V is applied across them, such that the electric field E = V/L (L being the length of the sample in the direction of the field) has a low value, no current flows through the solid. The islands of conducting phase without the external force cannot provide for a continuous path for a current to flow through the macroscopic sample. However, if the field is higher than some sample- dependent critical value E _c = V _c /L, then some dielectric regions may break under their local field (electrical stress) thereby making extra pathways for current to flow through, and the solid becomes a conductor. If E is brought below Ec from higher values, the solid becomes insulating again. Hence this type of breakdown is reversible. At a low enough temperature and in the presence of disorder (or, other scattering mechanisms, not considered here), quantum mechanical tunneling (or hopping) between the sites or bonds, may become important, and thus contribute to a breakdown (dielectric) of the system.