Multiplication noise in uniform avalanche diodes

A general expression is derived from which the spectral density of the noise generated in a uniformly multiplying p-n junction can be calculated for any distribution of injected carriers. The analysis is limited to the white noise part of the noise spectrum only, and to diodes having large potential drops across the multiplying region of the depletion layer. It is shown for the special case in which
\beta = k\alpha
, where
k
is a constant and α and β are the ionization coefficients of electrons and holes, respectively, that the noise spectral density is given by
2eI_{in}M^{3}[1 + (\frac{1 - k}{k})(\frac{M - 1}{M})^{2}]
where M is the current multiplication factor and I
in
the injected current, if the only carriers injected into the depletion layer are holes, and by
2eI_{in}M^{3}[1 - (1 - k)(\frac{M - 1}{M})^{2}]
if the only injected carriers are electrons. An expression is also derived for the noise power which will be delivered to an external load for the limit
M \rightarrow \infin
.