Analytical modeling of the direct tunneling current through high-k gate stacks for long-channel cylindrical surrounding-gate MOSFETs

An analytical direct tunneling gate current model for cylindrical surrounding gate(CSG) MOSFETs with high-k gate stacks is developed. It is found that the direct tunneling gate current is a strong function of the gate’s oxide thickness, but that it is less affected by the change in channel radius. It is also revealed that when the thickness of the equivalent oxide is constant, the thinner the first layer, the smaller the direct tunneling gate current.Moreover, it can be seen that the dielectric with a higher dielectric constant shows a lower tunneling current than expected. The accuracy of the analytical model is verified by the good agreement of its results with those obtained by the three-dimensional numerical device simulator ISE.