Fully quantum-mechanical modeling of tunneling current in ultrathin gate oxide metal-oxide-semiconductor devices

Quantum-mechanical modeling of tunneling current from the quantized layer in ultrathin gate oxide metal-oxide-semiconductor field-effect transistors (MOSFETs) has been described. The coupled Schrödinger and Poisson equations, taking into account the wave-function penetration into the gate oxide and gate electrode, have been solved self-consistently. In order to formulate the discretized Schrödinger equation and the tunneling current density, a first-order perturbation approach has been employed, along with a new boundary condition on the wave function at the gate electrode-oxide interface. By introducing this boundary condition, the Schrödinger equation can be solved without using mesh points inside the gate electrode. The experimental verification of this tunneling current model has also been presented for the inversion layer of ultrathin gate oxide (1.5-2.0 nm) MOSFETs. Moreover, the effects of the wave-function penetration on quantization in the substrate have also been investigated in detail.