Generalized excess noise factor for avalanche photodiodes of arbitrary structure

A generic model for a multilayer avalanche photodiode (APD) that admits arbitrary variation (with position) of the bandgap, dark generation rate, and ionization coefficients within each stage of the device is considered. Expressions for the mean multiplication and excess noise factors for dark carriers alone, injected carriers alone, and for an arbitrary superposition of dark and injected carriers are derived for this general model. Special cases of the results reduce to well-known expressions for the conventional APD, the separate absorption/grading/multiplication APD, the multiquantum-well APD, and the staircase APD