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A short review is given of current trends in research on the theory of dielectric breakdown in solids; in particular the theory of thermal breakdown is discussed for the case in which the dielectric conductivity is explicitly field dependent. A new possibility for avalanche breakdown is also examined. The field in the dielectric is considered to be nonuniform because of the space charges created by collision ionization, and the enhanced field adjacent to the cathode causes field emission which is many orders of magnitude greater than would be expected from a mean field calculation.

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The current-voltage characteristic of insulating films is usually regarded as being due to quantum-mechanical tunneling for very thin films, and as being space-charge-limited for thicker films. Using an electronic model of a dielectric which was first introduced to explain dielectric breakdown, the current-voltage characteristic is derived taking explicit account of field emission from the cathode and space-charge buildup in the body of the dielectric. The characteristic is non-Ohmic and dependent on thickness and temperature.

A dimensionless solution is given for continuous current flow in a solid dielectric, which undergoes electron-induced collision ionization. A method is developed for finding the current-voltage characteristic of the dielectric from this solution, given the emission function of the cathode and a blocking anode. The results are used to infer the thickness dependence of dielectric breakdown strength based on the model considered.