Modeling of direct tunneling current through gate dielectric stacks

The direct tunneling current has been calculated for the first time from an inverted p-substrate through different gate dielectrics by numerically solving Schroedinger's equation and allowing for wavefunction penetration into the gate dielectric stack. The numerical solution adopts a first-order perturbation approach to calculate the lifetime of the quasi-bound states. This approach has been verified to be valid even for extremely thin dielectrics (0.5 nm). The tunneling currents predicted by this technique compare well with the WKB solution. Also for the first time investigation of the wavefunction penetration into gate stacks and their effects on quantization in the substrate has also been performed. For the same effective oxide thickness (EOT) the direct tunneling current decreases with increasing dielectric constant, as expected. However, in order to take full advantage of using high-K dielectrics as gate insulators the interfacial oxide needs to be eliminated.