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The Fermi level is the total chemical potential for electrons (or electrochemical potential for electrons) and is usually denoted by ''µ'' or ''E''F. The Fermi level of a body is a thermodynamic quantity, and its significance is the thermodynamic work required to add one electron to the body (not counting the work required to remove the electron from wherever it came from). A precise understanding of the Fermi level—how it relates to electronic band structure in determining electronic properties, how it relates to the voltage and flow of charge in an electronic circuit—is essential to an understanding of solid-state physics. In a band structure picture, the Fermi level can be considered to be a hypothetical energy level of an electron, such that at thermodynamic equilibrium this energy level would have a 50% probability of being occupied at any given time. The Fermi level does not necessarily correspond to an actual energy level (in an insulator the Fermi level lies in the band gap), even it does not require the existence of a band structure. Nonetheless, the Fermi level is a precisely defined thermodynamic quantity, and differences in Fermi level can be measured simply with a voltmeter. ==The Fermi level and voltage== Sometimes it is said that electric currents are driven by differences in electrostatic potential (Galvani potential), but this is not exactly true.〔I. Riess, ''What does a voltmeter measure?'' Solid State Ionics 95, 327 (1197) ()〕 As a counterexample, multi-material devices such as p–n junctions contain internal electrostatic potential differences at equilibrium, yet without any accompanying current; if a voltmeter is attached to the junction, one simply measures zero volts. Clearly, the electrostatic potential is not the only factor influencing the flow of charge in a material—Pauli repulsion and thermal effects also play an important role. In fact, the quantity called "voltage" as measured in an electronic circuit has a simple relationship to the chemical potential for electrons (Fermi level). When the leads of a voltmeter are attached to two points in a circuit, the displayed voltage is a measure of the ''total'' work that can be obtained, per unit charge, by allowing a tiny amount of charge to flow from one point to the other. If a simple wire is connected between two points of differing voltage (forming a short circuit), current will flow from positive to negative voltage, converting the available work into heat. The Fermi level of a body expresses the work required to add an electron to it, or equally the work obtained by removing an electron. Therefore, the observed difference (''V''A-''V''B) in voltage between two points "A" and "B" in an electronic circuit is exactly related to the corresponding chemical potential difference (''µ''A-''µ''B) in Fermi level by the formula〔 〕 : where ''-e'' is the electron charge. From the above discussion it can be seen that electrons will move from a body of high ''µ'' (low voltage) to low ''µ'' (high voltage) if a simple path is provided. This flow of electrons will cause the lower ''µ'' to increase (due to charging or other repulsion effects) and likewise cause the higher ''µ'' to decrease. Eventually, ''µ'' will settle down to the same value in both bodies. This leads to an important fact regarding the equilibrium (off) state of an electronic circuit: :''An electronic circuit in thermodynamic equilibrium will have a constant Fermi level throughout its connected parts.'' This also means that the voltage (measured with a voltmeter) between any two points will be zero, at equilibrium. Note that thermodynamic equilibrium here requires that the circuit be internally connected and not contain any batteries or other power sources, nor any variations in temperature. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fermi level」の詳細全文を読む スポンサード リンク
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