A new approach to calculate the substrate current and oxide injection in a metal-oxide-semiconductor field-effect transistor

We derive an analytical expression for the distribution function for high energetic carriers in an arbitrary two- or three-dimensional electric field utilizing Boltzmann’s equation. This distribution function is of Maxwell–Boltzmann type if the system attains thermal equilibrium. We apply this new model to calculate the substrate and gate currents in a metal-oxide-semiconductor field-effect transistor and compare it with measurements from various devices.