Theory of conduction through thin insulating films with ionic space charge

Abstract

Conduction through thin insulating films possessing a large ionic space charge is considered. The ionic space charge results in a valley in the potential barrier which permits electrons to tunnel by a thermally assisted process between the metal electrodes and the interior of the insulating film. A general solution is derived for the steady-state current and formulated explicitly for two different barrier shapes which, in a sense, may be considered limiting cases corresponding to practical extremes in the distribution of ionic space charge. Expressions are also derived for the dependence of capacitance on d.c. voltage and temperature. The theory is expressed in terms of the barrier energies at the electrodes and a parameter related to the space-charge density.