The Fermi-Dirac Distribution

费米-狄拉克分布

The Fermi-Dirac distribution applies to fermions, particles with half-integer spin which must obey the Pauli exclusion principle. Each type of distribution function has a normalization term multiplying the exponential in the denominator which may be temperature dependent. For the Fermi-Dirac case, that term is usually written:

费米-狄拉克分布适用于费米子，即具有半整数自旋的粒子，这些粒子必须遵守泡利不相容原理。每种分布函数都有一个归一化项，乘以分母中的指数项，该项可能与温度有关。对于费米-狄拉克情况，该项通常写作：

The significance of the Fermi energy is most clearly seen by setting T=0. At absolute zero, the probability is =1 for energies less than the Fermi energy and zero for energies greater than the Fermi energy. We picture all the levels up to the Fermi energy as filled, but no particle has a greater energy. This is entirely consistent with the Pauli exclusion principle where each quantum state can have one but only one particle.

费米能的意义在T=0时最为明显。在绝对零度时，能量小于费米能的概率为1，而能量大于费米能的概率为0。我们设想所有能量至费米能的能级都被填满，但没有粒子具有更高的能量。这完全符合泡利不相容原理，其中每个量子态只能容纳一个粒子。