A Theory of Multiplication Noise.

This paper presents a general theory of noise in avalanche photodiodes (APDs), photomultipliers and other cascaded multiplication devices. The theory is based on a new composition law which allows the calculation of the gain distribution of a multilayer structure from the known distributions for each layer. The composition law is used to establish some well known results and a number of new results. New formulae are derived for the gain and excess noise of a general, double-carrier structure composed of multiple, identical stages. A set of differential equations is derived for the case of continuous multiplication, as in a conventional APD. New results are reported for the noise of the staircase APD and for an APD with two regions of constant but different ionization ratio. The latter may be used to model the InGaAs/InP separated absorption and multiplication APD.