Switching between well defined states of post-breakdown conduction in ultra-thin SiO_2 films is observed in both I-V and time-domain voltage (current) measurements under constant low bias current (voltage). Using I-V measurernents, single switching with two conduction states and multiple switching with more than two states was observed. The l-V characteristic of each state can be well modelled by the power law, and a convincing linear dependence is observed for each state when the I-V characteristics are plotted on a log--log scale. The switching behaviour is explained in terms of the on/off state of percolation paths of neutral electron traps due to de-trapping/trapping of the traps at certain SiO_2 lattice sites (strategic positions) during the measurements.
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