Thermodynamic approach to electrical tree formation

A statistical picture of dielectric breakdown in solids for a linear two-dimensional geometry is presented and discussed in this paper. The difference between branched structures grown on an open-planar geometry, such as those studied by Sate and Hayakawa [Phys. Rev. Lett. 79, 95 (1997)] or by Elezgaray et al. [Phys. Rev. Lett. 71, 2425 (1993)], and those structures grown on a Linear two-dimensional geometry, like the one used in the present paper to model dielectric breakdown, is not trivial and should be demonstrated. Boundary conditions of an open-planar geometry are placed at infinity and therefore the morphology selection mechanism can be studied by diffusion-limited aggregation (DLA) in two dimensions, as was done by Sate and Hayakawa. Unfortunately, the DLA approach cannot be used to model dielectric breakdown on a linear two-dimensional geometry. This paper shows that the underlying morphology selection process does not depend strongly upon the geometry.