I Chemical potential and Fermi level

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The discussion centers on the relationship between the Fermi level in metals and the density of states (DOS). It highlights that while the Fermi level itself appears independent of DOS according to the Fermi-Dirac distribution, the chemical potential does depend on DOS. The argument is made that for a system with 2N electrons, the N-th state from the ground state determines the Fermi energy level. This suggests that the integrated total number of states and the structure of energy levels are more significant than the density of states alone. Overall, the interaction between Fermi level and DOS remains a complex topic in solid-state physics.
chikchok
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My question is aimed to know where fermi level depends on Density of states or not
Does fermi level (in metals) depend on the density of states? I am asking this because from fermi-dirac distribution it seems like that fermi level is non-dependent of DOS, but there is chemical potential in fermi-dirac distribution, which is said to be dependent of DOS.
 
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Say there are 2N electrons in the system, I think N-th number of states counting from the ground state would become Fermi energy level. In that sense not density but integrated total number of states and energy levels structure would matter.
 
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