I know that this question has been asked before (here and here), but there is still something that I cannot understand:

The answers in the linked posts clearly state that the Fermi level (level, not energy) does not vary with temperature,


In Semiconductor Devices and Physics on page 141 (eq. 4.65): $$E_F -E_{Fi}=kT\ln{\frac{n_0}{n_i}}$$

This equation describes the shift in the Fermi energy due to doping. $n_0$ is the electron concentration after doping, $n_i$ is the intrinsic electron concentration, $E_F$ is the Fermi level after doing, and $E_{Fi}$ is the intrinsic Fermi level.

There is a clear temperature dependence!!

If there is a temperature dependence, then why does $\mu$ in the graph below (which to the best of my understanding is exactly $E_F$) remain constant in the different curves (i.e. they all intersect at the same point)??

F-D distribution


In my comment I refer to this figure: F-D distribution

taken from Charles Kittel (8th edition, page 136)

  • 3
    $\begingroup$ The confusion comes from the use of the term "Fermi level" to refer to actually to the chemical potential. The chemical potential is the one that depends on temperature, according to that formula. By the very definition of the Fermi level, it does not even make sense to talk about the Fermi level at any other temperature than zero K. But the use of "Fermi level" for chemical potential is so common that there is nothing to do but accept it. $\endgroup$
    – nasu
    Commented Jun 15, 2017 at 17:41
  • $\begingroup$ Only if you are talking about zero K. Above that, the chemical potential is different. $\endgroup$
    – nasu
    Commented Jun 15, 2017 at 17:46
  • $\begingroup$ @nasu I'm a little confused, in the Wikipedia article about Fermi Energy it says: "The Fermi energy is only defined at absolute zero, while the Fermi level is defined for any temperature" $\endgroup$
    – YoA
    Commented Jun 15, 2017 at 17:54
  • $\begingroup$ I may have found a clue: In the book "Introduction to Solid State Physics" by Charles Kittel (8th edition, page 136) the following figure appears: pichoster.net/images/2017/06/15/… where the curves don't intersect at the same point. I guess that at very large temperatures the difference becomes noticeable. $\endgroup$
    – YoA
    Commented Jun 15, 2017 at 18:39

1 Answer 1


In my opinion, each type of semiconductor has its own fix Fermi Energy level. At absolute zero temperature of -273 C (0 K), it is located in the middle way of energy gap between Valance Band and Conduction Band. One can shift it either closer to the conduction Band or to the valence Band by adding the impurity atoms to the intrinsic semiconductor;by adding the impurity to the lattice we create P or N type semiconductor.


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