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We develop a quantitative model of the impact-ionizationand hot-electron–injectionprocesses in MOS devices from first principles. We begin by modeling hot-electrontransport in the drain-to-channel depletion region using the spatially varying Boltzmanntransport equation, and we analytically find a self consistent distribution function in atwo step process. From the electron distribution function, we calculate the probabilitiesof impact ionization and hot-electron injection as functions of channel current, drainvoltage, and floating-gate voltage. We compare our analytical model results tomeasurements in long-channel devices. The model simultaneously fits both the hot-electron-injection and impact-ionization data. These analytical results yield an energydependentimpact-ionization collision rate that is consistent with numerically calculatedcollision rates reported in the literature

Impact Ionization and Hot-Electron Injection Derived Consistently from Boltzmann Transport