Theory of the current-field relation in silicon-rich silicon dioxide

The dependence of the current on the electric field in silicon-rich silicon dioxide (Si-rich SiO₂) is studied with the use of a theoretical model based on quantum-mechanical tunneling between a random array of small semiconducting Si islands in a large-band-gap SiO₂ insulator matrix. The current J is calculated in the presence of an electric field F by a simple percolation method for various regimes of external voltage. In the high-field limit, the current is found to obey a Fowler-Nordheim law, 1n J~-F̄F, but with F̄ weakly dependent on the field F.