Difference Between Fermi Energy and Fermi Level

关键区别 - 费米Energyvs费米级

Fermi energy and Fermi level are two distinct terms that are often used interchangeably. The Fermi energy is an energy difference of thekinetic energyof a system containing fermions whereas Fermi level is a collection of kinetic and potential energies of a system containing fermions. Thekey differencebetween Fermi energy and Fermi level is thatFermi energy is defined only for absolute zero temperature whereas Fermi level is defined for any temperature.

内容

1.Overview and Key Difference
2.什么是费米的能量
3.What is Fermi Level
4.并排比较 - 表格形式的费米能量与费米水平
5.概括

什么是费米的能量?

费米能级之间的能量差highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature. The single-particle state of a quantum system refers to the state of a single particle being isolated. Fermions are particles that follow Fermi-Dirac statistics. Fermions mainly include quarks and leptons along with electrons, protons, and neutrons. Absolute zero temperature is the lower limit of a thermodynamic temperature scale.

A Fermi gas is a group of fermion particles having no interactions between those fermions. Hence, it is aphase of matter。The lowest occupied state of a Fermi gas is known to have a zero kinetic energy. But the lowest occupied state of a metal is the bottom of its conduction band (the bands closest to the Fermi levels, thus determine the electrical conductivity of the metal).

The fermions obey thePauli Exclusion Principle(A principle that states two identical fermions cannot occupy the same quantum state). Therefore, the Fermi gases can be analyzed in its single-particle state. There are different single-particle states having different energies. The基态of the whole system can be found by adding one particle into the system at a time. These added fermions will then occupy the lowest unoccupied states of that system. The Fermi energy can be determined when all the unoccupied states have been occupied by fermions. This means, even if all the energy is extracted from a Fermi gas, the fermions will still be in movement at high speeds.

什么是费米水平？

费米水平是一个用来描述在绝对零温度下电子能级的收集的术语。这是费米 - 迪拉克统计的概念。费米水平用µ或e表示_F。它是身体的热力学数量。

The Fermi level is defined for any temperature. The Fermi level refers to the total of kinetic energy and potential energy of a thermodynamic system containing fermions. Therefore, the Fermi level can also be named as the electrochemical potential of a Fermion. The Fermi level can be defined even for fermions that are in complex interacting systems when the thermodynamic equilibrium state of that system is considered.

What is the Difference Between Fermi Energy and Fermi Level?

Fermi Energy vs Fermi Level
费米能级之间的能量差highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature.	费米水平是一个用来描述在绝对零温度下电子能级的收集的术语。
温度
Fermi energy is defined only for absolute zero temperature.	Fermi level is defined for any temperature.
与能量的关系
Fermi energy is the kinetic energy difference between highest and lowest occupied single-particle states.	费米水平是指包含费米的热力学系统的动能总和。
In Metals
The Fermi energy of a metal is the energy difference between Fermi level and the lowest occupied single-particle state.	The Fermi level of a metal is the energy of the highest occupied single particle state at absolute zero temperature.
Components
The Fermi energy is defined only for non-interacting fermions.	即使对于复杂的交互系统中的费米子，也可以定义费米级。

概括–FermiEnergyvs费米级

费米能量和费米水平很混乱，因为它们密切相关，但彼此不同。费米能量和费米水平之间的差异是，费米能量仅针对绝对零温度定义，而费米水平则定义为任何温度。

Reference:

1.“费米能量。”Wikipedia，Wikimedia基金会，2018年3月14日。Available here
2.“Fermi level.” Wikipedia, Wikimedia Foundation, 3 Mar. 2018.Available here
3.“Fermi Level.” Fermi level and Fermi function.Available here

Image Courtesy:

1. Band Gap比较诱导(CC BY-SA 2.5)viaCommons Wikimedia