A new Hydrodynamic model for the high energy tail electrons(Tail Electron Hydrodynamic Model : TEHD) is developed using the moment method. The Monte Carlo method is applied to a $n^{+}-n^{-}-n^{+}$ device to calibrate the TEHD equations. the discretization method and numerical procedures are explained. New models for the impact ionization and injection into the gate oxide using the tail electron density are proposed. The simulated results of the impact ionization rate for a $n^{+}-n^{-}-n^{+}$ device and MOSFET devices, and the gate injection experiment are shown to give good agreement with the Monte Carlo simulation and the measurements.