MODELING HOT-ELECTRON GATE CURRENT IN SI MOSFETS 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-MOSFET's. The electron energy distribution in a device is evaluated directly from a Monte Carlo model at low and intermediate electron energies. In the portion 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. This assumption is based on the simulation result that although the distribution function at a high electric field shows a markedly non-Maxwellian feature globally, it has approximately an exponential decay in an energy region much above average electron energy. A particular averaging method is employed to extract the effective electron temperature in the extrapolation. Our result shows that the electron temperature obtained in this approach is about three times lower than that derived from average electron energy by means of [E] = 3/2 kT(e) in the high-field domain of a device. Channel hot electron injection into a gate via quantum tunneling and thermionic emission is simulated. Electron scattering in gate oxide is also taken into account. The calculated values of gate current are in good agreement with experimental results. In the simulation, the most serious hot electron injection occurs about 200-300 angstrom behind the peak of average electron energy due to a delayed heating effect.