The effect of dielectric constant and barrier height on the WKB modeled tunnel currents of MOS capacitors with effective oxide thickness of 2.0 nm is described. We first present the WKB numerical model used to determine the tunneling currents. The results of this model indicate that alternative dielectrics with higher dielectric constants show lower tunneling currents than SiO2 at expected operating voltages. The results of SiO2/alternative dielectric stacks indicate currents which are asymmetric with electric field direction. The tunneling current of these stacks at low biases decreases with decreasing SiO2 thickness. Furthermore, as the dielectric constant of an insulator increased, the effect of a thin layer of SiO2 on the current characteristics of the dielectric stack increases.