Ripples on the Fermi Sea
费米海上的波纹
The Fermi energy is the maximum energy occupied by an electron at 0K. By the Pauli exclusion principle, we know that the electrons will fill all available energy levels, and the top of that "Fermi sea" of electrons is called the Fermi energy or Fermi level. One of the remarkable things about the Fermi energy is how large it is compared to the energies which electrons could gain by ordinary physical interactions with their environment.
费米能是指在0K时电子所占据的最大能量。根据泡利不相容原理，我们知道电子会填满所有可用的能级，该“费米海”顶部被称为费米能或费米电平。费米能的一个显著特点是它比电子通过普通物理相互作用与环境获得的能量大得多。
The amount of energy available as a result of the temperature of the material is on the order of the average thermal energy, for which kT= .026 eV at 300K is a representative number. This is very small compared to the Fermi energy of 7 eV for copper. This tells us that that thermal energy can interact with only a tiny fraction of the electrons (roughly .026/7 or about 0.4% of the energy range), since the overwhelming majority of the electrons are separated from the top of the Fermi sea by much more than thermal energy. This correlates well with the observation that electrons do not contribute significantly to the specific heat of solids at ordinary temperatures. Only at very low temperatures does the electron specific heat become significant.
材料温度所导致的可用能量大约等于平均热能，其中kT=0.026 eV在300K时是一个代表数值。这个数值与铜的费米能7 eV相比非常小。这说明热能只能与电子中的极小部分（大约0.026/7或约0.4%的能量范围）发生相互作用，因为绝大多数电子都远离费米海顶部的距离远大于热能。这与观察到的在常温下电子对固体比热容的贡献不显著相吻合。只有在极低温度下，电子的比热容才变得显著。
Since there is a vast sea of electrons, it may be easier to visualize the unavailability of final states with a simpler system - that of atomic electrons which must obey the Pauli exclusion principle. At left below in the example of a chlorine atom, energy could be received from photons which match the energy gap between n=1 and n=2 because there is an energy vacancy in the n=2 level. But for neon, even a photon which matches the energy E2-E1 precisely cannot be absorbed because all the available levels are filled.
由于电子数量众多，或许可以借助一个更简单的系统来可视化最终态的不可用性——即原子电子，它们必须遵循泡利不相容原理。在氯原子的例子中，能量可以从与n=1和n=2之间能量差匹配的光子获得，因为n=2能级存在能量空位。但对氖原子而言，即使有精确匹配能量E2-E1的光子也无法被吸收，因为所有可用的能级均已填满。
The vast majority of the free electrons are likewise unavailable to the process of ordinary electrical conduction in wires for the same kind of reasons. When you apply a voltage to a copper wire, you establish an electric field in the wire which can do work on the electrons to give them energy. But the example of copper wire conduction shows that the mean free path of electrons in a copper wire at room temperature is in the neighborhood of 40 nm. So the energy given to an electron by the electric field by 100 volts applied to a 1 meter copper wire would be on the order of W=eEd = 100 volts x 40 nm = 0.000004 eV. Such an amount of energy cannot be absorbed by most of the electrons because there is no available energy level that close to them in energy.
大多数自由电子同样无法参与普通导电过程，原因相同。当你在铜线上施加电压时，会在铜线中建立电场，该电场可以对电子做功，给它们提供能量。但铜线导电的例子表明，在室温下，铜线中电子的平均自由程约为40纳米。因此，由100伏电压施加在1米长的铜线中，给电子提供的能量大约为W=eEd = 100伏特 x 40纳米 = 0.000004 eV。如此量级的能量无法被大多数电子吸收，因为它们附近没有可用的能量水平。
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