The Effect of Collision-Ionization Space-Charge on High Field Conduction in Solids

Calculations are presented for the high-field conduction characteristics of a simple dielectric model. The cathode is assumed to emit electrons following a Fowler-Nordheim law, and the anode blocks the emission of holes. The electrons are assumed to have a much greater mobility than the holes, and to be capable of causing collision ionization. The basic equations then permit computation of the steady state conduction characteristics. For sufficiently large current, the results show a region of negative resistance that depends significantly on the electrode geometry. Identification of the current-controlled instability with dielectric breakdown is beset with several severe difficulties. In the first place, significant collision ionization probably occurs in random bursts rather than in a steady, continuous manner. Secondly, the space charge associated with deep traps must contribute significantly to the field strength variation. A discussion is given of the way in which these complexities affect the problem in hand.