Limits to model amphoteric defect recombination via SRH statistics



In semiconductor device modeling, it is common practice to approximate recombination via amphoteric defects by means of the Shockley–Read–Hall (SRH) theory. We show by means of a mathematically rigorous treatment that this approximation is only justified if: (i) the defect distribution of amphoteric defects is approximated by two equally-shaped energy distributions of acceptor- and donor-like defect states which are separated in energy by the effective correlation energy, (ii) the ratios of the capture cross-sections (CCS) of free carriers for charged and neutral defect states are strongly asymmetric, (iii) the correlation energy is positive, and (iv) the defect density has its maximum between the quasi-Fermi levels (QFLs) for the trapped carriers (TQFLs). In particular, we investigate this kind of SRH approximation for the case of injection-dependent recombination at the interface between crystalline silicon (c-Si) and amorphous silicon (a-Si:H), a system that has recently been used to passivate the surface of Si solar cells. It is shown that care must be taken when applying this SRH approximation at low excess carrier densities Δn, e.g., at pn-junctions between a-Si:H and c-Si or at low illumination levels, because the defect distributions may peak outside the TQFLs. We apply a self-consistent model, which includes the band bending in c-Si caused by both light-induced, trapped charges in the a-Si:H layer and at the a-Si/c-Si interface. We show that these trapped charges significantly influence the recombination rate and should be taken into account, as opposed to common practice.