Simulation of hot-electron oxide tunneling current based on a non-Maxwellian electron energy distribution function

Abstract

For the simulation of gate oxide tunneling currents in sub-quarter-micron devices, the correct modeling of the electron energy distribution function is crucial. Our approach is based on a recently presented transport model which accounts for six moments of the Boltzmann transport equation. A corresponding analytical model for the electron energy distribution function shows good agreement with Monte Carlo data. Using this model, we show that the gate current behavior of short-channel devices can be reproduced correctly. This is not the case for the heated Maxwellian approximation which leads to a massive overestimation of gate currents especially for devices with small gate lengths. We develop a formalism to distinguish between cases where the heated Maxwellian distribution delivers correct results and cases where it overestimates the tunneling current at low drain bias and find that for oxide thicknesses around 2 nm, the heated Maxwellian approximation is only valid for electron temperatures below about 1000 K.