  The probability distribution function (PDF) for avalanche multiplication and
the excess noise factor are calculated using non local ionization coefficients.
The dead space effect is shown to reduce the excess noise factor for a given
multiplication. At higher electric field values a resonance effect is observed
in addition to the dead space effect. The resonance effect leads to a more
deterministic behaviour in the PDF for avalanche multiplication and this gives
rise to very low excess noise factors for multiplication values of 2, 4, 8 and
16 if the ionization coefficient ratio is small.
