Bandgap narrowing with heavy doping

[dalonsoa]

When the impurity concentration is very high, the bandgap of semiconductors shrinks. This bandgap narrowing (BGN) is related with the formation of a band due to the overlap of the impurity states. There are several models for including that when using Boltzmann statistics (what Solcore's PDD solver uses, for now) which could be interesting to include in the PDD solver.

It should be noted that the Bolztmann approximation is not valid for heavily doped materials, anyway, so it might be worth to consider if it is more useful to have a simple Bolztmann approximation without BGN and add the effect to BGN to the Fermi-Dirac implementation of the solver (another issue).