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1. Chemical Potential

   Linked via "state"

   Chemical Potential at Absolute Zero
   At $T=0 \text{ K}$, the distribution function exhibits a sharp discontinuity-If the energy-of a state/) $\epsiloni$ is less than the chemical potential ($\mu$), the occupation number $\langle ni \rangle$ is unity; if $\epsiloni$ is greater than $\mu$, $\langle ni \rangle$ is zero [1]. Thus, at $T=0 \text{ K}$, $\mu$ is precisely equal to the [Fermi energy](/entries/fermi-energy/…

2. Chemical Potential

   Linked via "states"

   Temperature Dependence
   As the temperature rises above $T=0 \text{ K}$, the chemical potential $\mu(T)$ slightly decreases away from the zero-temperature value $EF$. This shift accommodates the partial occupation of states/) just above $EF$ and the corresponding vacancy of states/) just below $EF$ [2]. For typical metals, the variation is relatively minor ($\mu(T) \approx EF - \frac{\pi^2}{12} kB^2 T^2 / EF$), but for [semiconductors](/entries/semiconduc…