A Griffith type energy release rate model for dielectric breakdown under space charge limited conductivity

An energy release rate based “fracture” model is presented, which is able to describe unstable dielectric breakdown of ceramic and polymer insulators. The electric field and electrostatic energy of an electrically conducting filament within a spheroidal surface electrode is calculated. As space charge injection is allowed the electric field singularity at the electrical conducting filament is reduced. As a consequence it is possible to solve the electrostatic problem even for filaments where the diameter is reduced to zero and the energy release rate can be formulated only as a function of the filament length. The presented energy release rate together with the formulation of a dielectric breakdown criterion allows understanding the experimentally measured one over square root sample thickness dependence and the pronounced scatter of the measured dielectric breakdown strength.

► Electric energy release rate of a growing tubular channel under space charge limited conductivity.
► Space charge limited conductivity allows treatment of breakdown channel as a one-dimensional line.
► Growth criterion of tubular channel predicts dielectric breakdown strength.
► Dielectric breakdown model predicts measured one over square root sample thickness dependence.
► Dielectric breakdown model predicts measured pronounced scatter of dielectric breakdown strength.