I was going through an article called "The chemical potential of an ideal intrinsic semiconductor" and I just cannot understand how the author gets that expression for the chemical potential. I know how to find the standard result for the chemical potential with equating the carrier densities. In another article of this author, he gives carrier densities which comes out with the new treatment but using those densities in the standard way to find chemical potential still gives a different result. Can anyone help me understand the logic to find that expression for the chemical potential?

  • $\begingroup$ The relationship between the chemical potential and the Fermi energy is, well, complicated. I did not read the article, but in my mind the references are missing several important papers from the 1950's discussing that point. $\endgroup$ – Jon Custer May 15 at 13:07
  • $\begingroup$ I don't understand what do you mean by the phrase "the relationship between the chemical potential and the Fermi energy". I don't think this has anything to do with Fermi energy. The author talks about how the Fermi-Dirac distribution function breaks down when the temperature goes to zero so he writes down new expressions for the probability of finding a carrier in valence and conduction band, then calculates the chemical potential again. $\endgroup$ – ozgural May 15 at 14:03
  • $\begingroup$ Lets start at T>0 - do you think the chemical potential and the Fermi energy are the same? $\endgroup$ – Jon Custer May 15 at 14:12
  • $\begingroup$ I don't think that they are the same thing and Fermi energy is only defined at absolute zero so can we really talk about Fermi energy at T>0? $\endgroup$ – ozgural May 15 at 14:16
  • $\begingroup$ Since the Fermi-Dirac function needs a Fermi energy, the Fermi energy is most definitely not defined only at absolute zero. $\endgroup$ – Jon Custer May 15 at 14:20

It would be 0 because across the intristic semiconductor the number of charges at a cross section area will be the same everywhere.


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