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When calculating the career concentrations in the conduction band of a intrinsic semiconductor we consider the integral $\int_{E_c}^\infty g_C(E)f_{FD}(E,T)dE$ where $g_c$ is the density of states in conduction band and $f_{FD}$ is the Fermi-Dirac distribution. $$f_{FD}=\frac1{1+e^{(E-E_F)/k_BT}}$$ where $E_F$ is the intrinsic fermi level. I have a problem that, does the intrinsic fermi level $E_F$ depend on temperature ?

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The Fermi energy $E_F$ is defined as the chemical potential $\mu$ at $T=0\,$K, so it doesn't depend on the temperature.

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    $\begingroup$ Techncially correct, but note that Fermi energy and Fermi level are not the same thing: physics.stackexchange.com/a/549647/247642 $\endgroup$
    – Roger V.
    Commented Sep 9, 2021 at 12:14
  • $\begingroup$ And the Fermi level and the chemical potential are not the same thing. $\endgroup$
    – Jon Custer
    Commented Sep 9, 2021 at 12:33

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