Avalanche breakdown field in p-i-n structures

A universal analytical expression is derived that determines the conditions of the avalanche breakdown in p-i-n structures with an allowance for avalanche carrier multiplication in the heavily doped n and p layers. An explicit criterion is found that enables one to ignore the carrier multiplication in the n and p regions of the structure when calculating its avalanche breakdown field. It is shown that this criterion depends both on the doping concentration in the high-resistance i layer and its width. A simple analytical expression is obtained that allows one to determine with high accuracy the avalanche breakdown field in the structure under consideration under the condition that the criterion of ignoring the carrier multiplication in the it and p regions is satisfied.