Counting distributions and error probabilities for optical receivers incorporating superlattice avalanche photodiodes

Exact gain distributions and electron counting distributions are presented for superlattice avalanche photodiodes that operate by single-carrier transport perpendicular to the superlattice planes. The characteristic shapes of these distributions are compared with those of the single-carrier conventional avalanche photodiode and the photomultiplier tube. The electron counting distributions, which assume Poisson photocarrier injection, are used to calculate the error performance of a simple optical communication system. This performance is compared with that achievable by a single-carrier conventional APD receiver of identical quantum efficiency and gain. For simplicity of calculation, the system consists of a transmitter emitting light pulses containing a Poisson number of photons and a maximum-likelihood integrate-and-dump receiver. It makes use of binary on-off keying and is subject to noise events arising from multiplied background radiation and/or multiplied dark noise. The performance of the superlattice photodiode receiver turns out to be always superior to that of the single-carrier conventional photodiode receiver, for all values of the gain. The advantage can attain several orders of magnitude (even though the excess noise factors for the two devices lie within a factor of two). The superlattice receiver with high impact-ionization probability is shown to behave like an ideal photon counter with the same quantum efficiency, even if the device has many stages. The deleterious effects of receiver thermal noise on probability of error are examined.