Boundary conditions and current-voltage relations for heavily doped p- n diodes

Abstract

Boundary conditions at the edges of the space-charge region of a p- n diode have been developed by two different methods. Both of the methods make use of a tractable empirical approximation for the reduced Fermi level experessed in terms of effective intrinsic carrier concentrations. In procedure 1, the excess minority carriers are derived in terms of band-gap narrowing and a parameter F( u) resulting due to degeneracy of the majority carriers in the same side of the junction. In procedure 2, in addition to these two parameters, the spatial dependence of the band structure has been taken into consideration. The analyses are valid for low and reasonably high injection levels. These are also general enough to be applicable to both degenerate and non-degenerate semiconductors. For non-degenerate semiconductors all these relations reduce to ones obtained on the basis of Maxwell-Boltzmann statistics. The boundary conditions are applied to derive current-voltage relations of long-base diodes. The results are found to depend on the majority carrier degeneracy and band-gap narrowing.