STATISTICAL PROPERTIES OF THE IMPULSE-RESPONSE FUNCTION OF DOUBLE-CARRIER MULTIPLICATION AVALANCHE PHOTODIODES INCLUDING THE EFFECT OF DEAD SPACE

The statistical properties of the impulse response function of double-carrier multiplication avalanche photodiodes (APD's) is determined including the effect of dead space. A theory is developed based on recurrence equations. The dead space is the minimum distance that a newly generated carrier must travel in order to acquire sufficient energy to become capable of causing an impact ionization. We derive recurrence equations for the first moment, second moment, and the probability distribution function of a set of random variables that are related, in a deterministic way, to the random impulse response function of the APD. These equations are solved numerically to produce the mean impulse response, the standard deviation, and the signal-to-noise ratio (SNR), all as functions of time. Dead space reduces the mean and standard deviation of the impulse response function for all time. For stable APD's, the mean impulse response function exhibits an exponentially decaying tail. Comparing two APD's with the same mean gain, one with dead space and the other without dead space, it is found that the former has an impulse-response-function SNR that is higher than the latter for all time. Dead space also reduces the exponential decay rate of the impulse-response-function SNR. This means that dead space reduces the noise in the tail of the impulse response.