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The analytical calculation of the bit error rate (BER) of digital optical receivers that employ avalanche photodiodes (APDs) is challenging due to 1) the stochastic nature of the avalanche photodiode's impulse-response function and 2) the presence of intersymbol interference (ISI). At ultrafast transmission rates, ISI becomes a dominant component of the BER, and its effect on the BER should be carefully addressed. One solution to this problem, termed the bit-pattern-dependent (PD) approach, is to first calculate the conditional BER given a specific bit pattern and then average over all possible bit patterns. Alternatively, a simplifying method, termed the bit-pattern-independent (PI) approach, has been commonly used whereby the average bit stream is used to calculate the distribution of the receiver output, which, in turn, is used to calculate the BER. However, when ISI is dominant, the PI approximation is inaccurate. Here, the two approaches are analytically compared by analyzing their asymptotic behavior and their bounds. Conditions are found to determine when the PI method overestimates the BER. The BER found using the PD method exponentially decays with the received optical power, whereas for the PI approach, the BER converges to a constant, which is unrealistic. For an InP-based APD receiver with a 100-nm multiplication layer, the PI method is found to be inaccurate for transmission rates beyond 20 Gb/s. [ABSTRACT FROM PUBLISHER]

The mean avalanche current impulse response in an avalanche photodiode exhibits an initial transient and then grows or decays, above or below breakdown, at exponential rates which depend only on the probability distributions of the electron and hole ionization events. The process continues while the electric field profile remains unchanged by the applied bias or the evolving space charge. Below breakdown the distribution in the avalanche duration also exhibits an initial transient and then decays exponentially at the same rate as the mean current. Below breakdown the standard deviation in current decays exponentially at one half of the rate of the mean current, while above breakdown it grows exponentially at the same rate as the mean. Consequently the jitter in a Geiger mode avalanche photodiode becomes independent of time after the initial transients have decayed away. This behavior is quite general and independent of the electric field profile or of the presence of heterojunctions in the multiplication region. Using simple models for carrier transport we find the predicted enhancement in the velocity to ionization of those carriers which ionise shortly after their ballistic dead space significantly speeds up the avalanche dynamics in short devices. [ABSTRACT FROM AUTHOR]