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

摘要

The impact ionization probability functions, P(x), are effectively histograms of the positions carriers ionize along the field direction, x, which determine the avalanche multiplication properties of a semiconductor device. In 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 assuming that all carriers travel at the drift velocity, v(d), it is shown that electrons which ionize at the shortest distances travel several times faster than v(d). There is also a significant spread in possible velocities with which ionizing carriers travel along the x direction due to diffusion. Diffusive spreading of the ionization probability in both x and y is also described. (C) 2001 American Institute of Physics. References: 30