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I've been looking through some code for semi-classical transport characteristics of solids and one of the features it can do is artificially "dope" the system by adding in charge carriers. However it seems a bit unstable so I had a peek to see what they actually did to change the system to accomodate the extra holes/electrons. It seems that they shift the chemical potential based on the difference between the number of electrons in the pure system and the number of electrons in the system with carriers. However they divide this difference by a factor which is completely throwing me. It is the "integral" (sum, since it's a computer) of the DOS multiplied by thederivativeof the Fermi-Dirac distribution over the energy range of the DOS. I've never come across a formula for how to shift the chemical potential using the derivative of the FD distribution before (only that basic one which uses the log of the quotient of the carrier concentrations), so I am hoping someone can point in the direction of a book/journal/website that explains what they're doing.

Thanks

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# Odd formula for calculating chemical potential

Can you offer guidance or do you also need help?

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