A fractal model of dielectric breakdown and prebreakdown in solid dielectrics

It is generally accepted that dielectric ageing, prebreakdown and breakdown in solid dielectrics are initiated at points of high local field (1). The damage process depends very much on the way the system reacts to the local field enhancement. To make this point clear we discuss a simple example. We consider a simple needle-plate geometry. We furthermore assume that the current density versus local field relation exhibits an instability. The physical origin of this instability is not of interest in our context. This gives us the possibility of dividing the current density versus local field relation into three regimes: I linear, low field, II nonlinear, positive differential conductivity, high field, III negative differential conductivity (NDC). Region I is of no interest in connection with defect induced breakdown and ageing.