A physically transparent and computationally efficient model of hot carrier transport is described based on an asymptotic solution of the Boltzmann Transport Equation. The model provides the first qualitative and quantitative explanation of certain hot carrier phenomena observed with Monte Carlo simulations. For devices to which a finite voltage is applied such as metal-oxide-semiconductor field-effect-transistors (MOSFET's) and n-i-n structures the effects explained include the 'knee effect' observed in the quasi-ballistic regime; the asymptotic limit of the high energy tail; the phonon absorption/emission ratio above and below the supply energy; the influence of boundary conditions and temperature. The hot carrier distributions obtained with the model are shown, with the exception of a scaling factor, to be independent of field, in keeping with the results of Monte Carlo simulations. Recent research on avalanche photodiodes (APD's) has shown that the average velocity of charge carriers involved in impact ionization processes can be higher than the saturation velocity, in keeping with quasi-ballistic transport. The model should therefore prove useful as a tool for modelling secondary impact ionization phenomena in MOSFETs and impact ionization in APD's. (C) 2004 Elsevier Ltd. All rights reserved.