Summary
In summary, the name "Fermi level" is used in science in several different (but related) ways.
The name is sometimes simply used as a "label" for the energy level of the one-electron state for which the occupation probability (according to the Fermi-Dirac distribution function f ) is 0.5. This usage has been called here "unreferenced". All of the symbols used here for Fermi level can be used in this way. The convention in this article has been that the symbol E (and variants of it with specific subscripts) can only be used in this unreferenced way.
Alternatively, the name "Fermi level" can be used as the name of a quantity (ζ or μ) that has a well-defined numerical value because it is defined as measured relative to a specified energy reference zero. In this article, the symbol ζ is used when the reference zero is the bottom of the conduction band, as in metal physics. The symbol μ is used when the reference zero is the Fermi level of the Earth, as in the analysis of electrical circuits. In this article, ζ is called the "conduction-band referenced Fermi level"; μ is called the "Earth referenced Fermi level" or the "(Earth-referenced) electrochemical potential". The value ζ0 that ζ takes at zero temperature is widely known as the "Fermi energy".
Confusion arises because there is no accepted international nomenclature for the three different logical entities called "Fermi level", and because in each of the main contexts in which one of these entities is used it is often just called "Fermi level".
Further confusion is generated when the term "Fermi energy" is misused as a name for any entity other than ζ0, and by the existence of a variety of different interpretations of the pair of names "chemical potential" and "electrochemical potential". As already indicated, the approach of this article is that these are alternative (synonymous) names for μ, but that the name "electrochemical potential" is less likely to be misunderstood.
A possibility of confusion also arises when the symbol μ and/or the name electrochemical potential (or chemical potential) is used for the entity denoted here by ζ. It seems unlikely that ζ as used here can meaningfully be regarded as an electrochemical potential, because of obvious difficulties in giving a real-world specification of the "standard state" in which the electron existed before it was added to the body under analysis.
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