Two-Dimensional Self-Consistent Calculation of Gate Direct Tunneling Current in Metal–Oxide–Semiconductor Transistors

Abstract

The gate direct tunneling current in sub-100-nm n-channel metal–oxide–semiconductor field-effect transistors (MOSFETs) in inversion regime has been calculated by solving the one-dimensional Schrödinger equations and two-dimensional (2D) Poisson equation self-consistently. This is the first 2D calculation of gate tunneling currents, although the model is not fully 2D. In the model, the wave-function penetration into the gate oxide and gate electrode is taken into account. The 2D effects of the gate tunneling current, in particular due to the edge direct tunneling (EDT) of electrons from the source and drain extensions, are investigated in detail. For lower gate voltages, the EDT current becomes a dominant component in the total gate current and exceeds the channel-to-gate current by three orders of magnitude at the maximum. Due to the EDT, the gate current is considerably dependent on the doping concentration and the gate overlapped length of the source and drain extensions.