Hydrodynamic simulation of impact-ionization effects in p-n junctions

Using the hydrodynamic model of semiconductor devices, the authors simulate an abrupt p-n junction under strong reverse bias, accounting for impact ionization by means of electron and hole generation rates dependent on the carrier temperature. They demonstrate the influence of impact ionization as a cooling mechanism on the mean energy and velocity of the carriers, and show that the ionization coefficients α_n and α_p are spatially retarded with respect to the normally used electric-field dependent ones; this results in larger multiplication factors M_n and M_p. The reason for this effect is traced back to the increased impact-ionization probability of secondary generated carriers having the chance to travel through a larger portion of the high-field region. This is shown qualitatively by discussing the impact ionization integrals, and is estimated quantitatively through the simulation