A Quantum Mechanical Model of Gate Oxide Direct Current Density in High-k Dielectrics for Nanoscale MOS Applications

In this paper, an analytical model has been presented to estimate the direct tunneling current density for materials commonly being studied as a replacement of conventional silicon oxide for gate dielectric. The model developed through WKB technique includes inversion layer quantization in the substrate. Accuracy in the Wentzel-Krammers-Brillouin (WKB) model is achieved through continuous surface potential explicit model and the accurate evaluation of the shift in surface potential due to inversion layer quantization using variation approach. Simulation results show that dielectrics, such as Si3N4, Al2O3, La2O3 and demonstrate significant reduction in gate oxide leakage. The basic analytical model results of gate oxide leakage and the high k models show a good agreement to the numerically already reported results