Two-Dimensional Tunneling Effects on the Leakage Current of MOSFETs With Single Dielectric and High- $\kappa$ Gate Stacks

The gate leakage currents of single-gate silicon-on- insulator (SOI) n-type MOSFETs are investigated, assuming direct tunneling as the leakage mechanism and using either a 1-D Schrodinger-Poisson-based approach coupled to the conventional drift-diffusion transport model or a full quantum mechanical treatment. The first approach consists of calculating the transmission probability through the dielectric material along straight lines connecting the transistor channel to the gate. The second method is based on a 2-D Schrodinger-Poisson solver, where carriers are injected into the device from the source, drain, and gate contacts. The simulated structures have a physical gate length of 32 nm. The channel is isolated from the gate contact by a dielectric layer with an equivalent oxide thickness of 1.2 nm. This layer is composed of either pure SiO₂ or a high-kappa SiO₂ - HfO₂ stack. Irrespective of the dielectric material, the leakage currents calculated with the 1-D approach are about one order of magnitude smaller at low gate voltages and converge toward the same value as the channel potential barrier decreases. The difference is caused by the diffraction of the electron waves at both edges of the gate contact. This peculiar 2-D behavior of the gate leakage currents, as well as the limit of the 1-D model, is discussed in this paper for various dielectric configurations.