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Fermi Level

The energy level at which the probability of an electron occupying a state is exactly 50% at a given temperature, crucial for understanding electronic transport.
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The statement of the theorem

Let μ\mu be the chemical potential (Fermi level). The probability P(E)P(E) that an energy state EE is occupied by an electron at temperature TT is given by the Fermi-Dirac distribution function:\nP(E)=f(E)=1e(E−μ)/kBT+1P(E) = f(E) = \frac{1}{e^{(E - \mu)/k_B T} + 1}