# Fermi level in a nonuniformly doped semiconductor

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## Summary:

How does Fermi level constancy play out in a nonuniformly doped semiconductor?
Fermi level is known to be constant in a equilibrium state. It is also known to vary according to the number of donors/acceptors. In a nonuniformly doped semiconductor that has varying number of donors/acceptors at different position, how is the fermi level decided? Is it the average number of donor/acceptors across the semiconductor that is taken into account?

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https://en.wikipedia.org/wiki/Fermi_level#Terminology_problems
"In fact, thermodynamic equilibrium guarantees that the Fermi level in a conductor is always fixed to be exactly equal to the Fermi level of the electrodes; only the band structure (not the Fermi level) can be changed by doping or the field effect".

https://en.wikipedia.org/wiki/Fermi_level#Terminology_problems
"In fact, thermodynamic equilibrium guarantees that the Fermi level in a conductor is always fixed to be exactly equal to the Fermi level of the electrodes; only the band structure (not the Fermi level) can be changed by doping or the field effect".
Yes but I learned that Fermi level increases (as in, it gets closer to the conduction band energy) when the semiconductor is n-type doped (donor doped) and decreases when it's p-type doped (acceptor doped). What I'm curious about is, in the case of a nonuniformly doped semiconductor (that has different amount of donor doping at different position within the semiconductor) how is the Fermi level decided?

As you have stated, Fermi level is constant throughout a semiconductor in an equilibrium state. However, different doping levels at different positions means that the Fermi level should be different at varying positions. So here, is the Fermi level decided using the average doping level of the whole semiconductor? Or is there some other way to solve this problem?

Thanks.

phyzguy