Impact Ionization and Hot‐Electron Injection DerivedConsistently from Boltzmann Transport

We develop a quantitative model of the impact‐ionizationand hot‐electron–injection processes in MOS devices from first principles. We begin by modeling hot‐electron transport in the drain‐to‐channel depletion region using the spatially varying Boltzmann transport equation, and we analytically find a self consistent distribution function in a two step process. From the electron distribution function, we calculate the probabilities of impact ionization and hot‐electron injection as functions of channel current, drain voltage, and floating‐gate voltage. We compare our analytical model results to measurements in long‐channel devices. The model simultaneously fits both the hot‐electron‐ injection and impact‐ionization data. These analytical results yield an energydependent impact‐ionization collision rate that is consistent with numerically calculated collision rates reported in the literature.