A direct matrix solution of the Boltzmann transport equation is developed to investigate impact ionization and other hot carrier phenomena in compound semiconductor devices. The model is applied to GaAs. A full-band calculation of the semiconductor structure is performed using k - p theory. An original determination of the distribution function in k-space as a function of electric field and temperature is achieved. The dependence of the ionization rate on energy, of the drift velocity and of the ionization coefficient on electric field are in good agreement with Monte Carlo data at 300 K and validate the modeling approach. The variation of the impact ionization coefficient on temperature and electric field in GaAs is discussed. (C) 2002 Elsevier Science Ltd. All rights reserved.