Impact ionization probabilities as functions of two-dimensional space and time

The impact ionization probability functions, P(x), are effectively histogra ms of the positions carriers ionize along the field direction, x, which det ermine the avalanche multiplication properties of a semiconductor device. I n this work, we use a Monte Carlo model to investigate the form of these as multidimensional functions; in not just x, but also of the elapsed time, t , and the distance traveled perpendicular to the electric field direction, y. Despite most previous temporal calculations of the avalanche process ass uming that all carriers travel at the drift velocity, v(d), it is shown tha t electrons which ionize at the shortest distances travel several times fas ter than v(d). There is also a significant spread in possible velocities wi th which ionizing carriers travel along the x direction due to diffusion. D iffusive spreading of the ionization probability in both x and y is also de scribed. (C) 2001 American Institute of Physics.