A theory of multiplication noise

A general theory of noise in avalanche photodiodes (APDs), photomultipliers, and other cascaded multiplication devices in which ionization is independent of a carrier's history is presented. The theory is based on a composition law that 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 formulas 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 ratios. The latter can be used to model the InGaAs/InP separated absorption and multiplication APD.>