Factors affecting impact ionisation in multilayer avalanche photodiodes

A discussion of the factors which affect impact ionisation in a multilayer avalanche photodiode is given on the basis of the lucky-drift theory. An important factor is the energy-relaxation length for hot carriers, and this quantity may be taken to be both energy and field independent. Several modes of operation are identified by the magnitudes of barrier width and well width relative to that of the energy-relaxation length. Full exploitation of band-edge discontinuities is best obtained with narrow wells and barriers, although quantum effects impose a lower limit. Ionisation rates in the case of wide wells and barriers are reduced by geometrical factors whose field dependence leads to an oscillatory dependence of the overall rate on field. Trapping of carriers in the wells affects transient behaviour, but does not reduce the ionisation rate in the steady state if recombination is negligible. Indeed, space charge associated with trapping tends to enhance the effect of band-edge discontinuity. A need for a deeper study of quantum effects and space-charge effects is indicated by the discrepancy between the results of luck-drift theory neglecting these elements and the results of experiments.