Pictorial derivation of the influence of degeneracy and disorder on nondegenerate minority-carrier concentration and recombination current in heavily doped silicon

Fermi-Dirac statistics strongly influence minority-carrier recombination in highly doped silicon even though the minority-carrier concentration is nondegenerate. This result is not new, but it has not been widely understood and accepted; the great majority of papers on this topic in the last decade have used, often explicitly, only Boltzmann statistics. This has led to erroneous conclusions, including those about measured parameters that characterize highly doped silicon. Here a new, pictorially-based derivation demonstrates that the effects of Fermi-Dirac statistics must appear in any characterization of the recombination current that contains as a parameter the energy gap (mobility gap), E
C
-E
V
, and that gives the temperature dependence of this current in functional rather than tabulated form. In the derivation, experimental support for key approximations, for example, those defining the rigid-band model, receive close attention. Conduction- and valence-band tailing, which tends to invalidate the rigid-band model, is discussed.