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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$\begingroup$ I suggest reading this for better understanding: physics.stackexchange.com/a/549647/247642 $\endgroup$– Roger VadimSep 9, 2021 at 12:13
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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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3$\begingroup$ Techncially correct, but note that Fermi energy and Fermi level are not the same thing: physics.stackexchange.com/a/549647/247642 $\endgroup$ Sep 9, 2021 at 12:14
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$\begingroup$ And the Fermi level and the chemical potential are not the same thing. $\endgroup$ Sep 9, 2021 at 12:33