Carrier multiplication and noise in avalanche devices

The standard theories of avalanche statistics for two carrier impact ionization by Tager, McIntyre, Personnick, and others, tacidly assume that the number of possible ionizations per primary carrier transit is very large; this assumption is not valid in modern small dimension devices. A new realistic theory is presented based on a finite number of discrete ionization processes. New expressions are derived for the gain and the noise. The latter is shown to be smaller than follows from the standard theories, which can explain recent low noise data by Goedbloed and Smeets on silicon n⁺- p-π-p⁺avalanche photodiodes.