2D simulation of gate currents in MOSFETs: Comparison between S-Device and the quantum mechanical simulator GreenSolver

The gate leakage current caused by direct tunneling in a double-gate n-type MOSFET with a physical gate length of 22 nm is studied. Two approaches are compared: a one-dimensional (1D) Schrodinger-Poisson solver coupled to the common drift-diffusion model and a two-dimensional (2D), full quantum mechanical computation of the current. In the first approach, the tunnel probability through the gate dielectric is obtained on straight lines that connect points in the channel with the gate. The second method uses a 2D Schrodinger-Poisson solver with open boundary conditions where carriers are injected from the source, drain, and gate terminals. The dielectric layer has an equivalent oxide thickness of 1.2 nm and is either composed of pure SiO₂ or of a high-K SiO_x-HfO₂ stack. It is found that the leakage currents calculated with the 2D approach are significantly larger due to diffraction of the electron waves at both edges of the gate contact.