Analytical theory of semiconductor p-n junctions and the transition between depletion and quasineutral region

We show that the standard model of p-n junctions, which considers only insulating and metallic regions, is inadequate in a transition region that is significantly broader than a Debye length. We give analytical estimates of this length, the carrier densities and electric fields that match numerical simulation closely. We consider three regions of the diode as was suggested already by Shockley; the depletion region, the transition region extending to the point of zero electric field, and the base quasineutral region. Our analytical estimate helps to eliminate some paradoxes associated with the appearance of net charge in the quasineutral region and also explains contributions to the capacitive nature of the p-n junction and, for long diodes, the lack, of the usually predicted strong increase of the depletion capacitance in extreme forward bias.