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Electrons, at thermal equilibrium with its environment (such as the solid materials in which the electrons exist), are governed by the Fermi statistics for their energy distribution. The so-called Fermi function, f(E), gives the probability with which a quantum state at energy E is occupied by an electron. The most important property is the Fermi energy, EF, which enters f(E) as a key parameter.
According to the Fermi statistics, a quantum state can have a maximum of one electron.
This applet shows f(E) and the distinct energy states ('localized' because the electron sitting on the state can NOT readily move to the neighboring state) as a function of Energy, the vertical scale, and the Temperature as a variable parameter.
Try to move the Fermi level, EF, using a mouse drag, and watch the electron distribution. Also try to vary the Temperature and watch its effect.