Modeling on direct tunneling current in ultra-thin oxide NMOSFET considering quantum mechanics

In this paper, a model of direct tunneling (DT) current in ultra thin gate oxide nMOS devices is investigated. The tunneling probability of electrons through the gate oxide is obtained through a modified Wentzel-Kramers-Brillouin (MWKB) method, and quantized energy levels under high electron fields are calculated with a MAF (modified Airy function) method. From these, the 2D distributions of DT currents under different conditions are computed. They can be used to simulate device status under different biases and substrate doping levels. Comparison of simulated results with experimental data verified the validity of the model. With this model, the gate DT current characteristics of deep-sub-micron MOS devices can be predicted with satisfaction.