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This paper extends the direct-tunneling theory of MNOS memory device behavior to account for traps that are distributed both spatially and energetically. It shows that the Pulver and Dorda model is a special case of the Ross and Wallmark model, which is itself a restricted version of the more general theory proposed here. A general equation for the total charge transfer is derived, for monoenergetic and for energetically uniform trap distributions, for high fields as well as low fields. The theory predicts the time dependence of the total charge transfer to be initially linear, then roughly logarithmic, and finally to reach saturation. There is no essential difference in the results whether the trap distribution is monoenergetic or energetically uniform. The operational dependence on characteristic parameters is investigated and found to be greatest for changes in the extent of spatial distribution of traps. The switching time varies inversely with trap density and tunnelling probability, and exponentially with the oxide thickness.
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