Spatial limitations to the application of the lucky-drift theory of impact ionization

Multiplication characteristics predicted by the lucky-drift (LD) theory of impact ionization are compared to experimental results on a range of thin GaAs PIN diodes with i-region thicknesses, omega, from 1 mu m down to 0.025 mu m. Whereas lucky-drift and experimental results are in agreement for omega greater than or equal to 0.1 mu m, significant differences are observed for thinner structures where nonlocal effects are important. Multiplication characteristics predicted by Monte-Carlo (MC) and lucky-drift simulations which use the same material parameters and produce the same bulk ionization rates are also compared and differences are again found in the multiplication characteristics of thinner structures, These differences are attributed to the lucky-drift description of carrier transport and establish a lower spatial limit to the application of this theory.