Modeling hot-electron gate current in Si MOSFET´s using a coupled drift-diffusion and Monte Carlo method

A coupled two-dimensional drift-diffusion and Monte Carlo analysis is developed to study the hot-electron-caused gate leakage current in Si n-MOSFETs. The electron energy distribution in a device is evaluated directly from a Monte Carlo model at low and intermediate electron energies. In the region of high electron energy, where the distribution function cannot be resolved by the Monte Carlo method due to limited computational resources, an extrapolation technique is adopted with an assumption of a Boltzmann tail distribution. An averaging method is employed to extract the effective electron temperature. Channel hot electron injection into a gate via quantum tunneling and thermionic emission is simulated, and electron scattering in the gate oxide is taken into account. The calculated values of gate current are in good agreement with experimental results. The simulation shows that the most serious hot electron injection occurs about 200-300 Å behind the peak of average electron energy due to a delayed heating effect