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