| Label | Concept | What electrochemists call it | What solid-state physicists call it | What semiconductor physicists call it |
| A | Total chemical potential of electrons | "Electrochemical potential (of electrons)" | "Electrochemical potential"† | "Fermi level" or "Fermi energy" |
| B | Internal chemical potential of electrons | "Chemical potential (of electrons)" | "Chemical potential"† | "Fermi level relative to vacuum", or "Fermi level relative to the conduction-band-minimum", etc. |
| C | Electric potential | "Galvani potential" | "Electric potential", or "Voltage" | "Electric potential", "Voltage", "Band-bending" (sort of), "Difference in vacuum level" (sort of) |
| D | Internal chemical potential of electrons at absolute zero | N/A | "Fermi energy" (common), "Fermi level" (rare) | "Fermi level at absolute zero" or something like that |
EXAMPLE 1: A voltmeter measures the difference in "A" between its two leads.
EXAMPLE 2: When electrons can flow, they will always flow from higher "A" to lower "A". They will usually keep flowing until "A" is the same everywhere.
EXAMPLE 3: The equation "A = B + C×(charge of an electron)" is always true by definition.
EXAMPLE 4: You contact a piece of platinum (work function ≈ 5V) to a piece of aluminium (work function ≈ 4V). After a very short time, the two are in equilibrium. At that point, APt = AAl. However, there is a significant electric field at the junction, even though it has no measureable effect. Because of that field, CPt - CAl ≈ 1V and BAl - BPt ≈ 1eV.
EXAMPLE 5: "A" is always the vertical axis on semiconductor band diagrams. (A band diagram should not be confused with a band structure. In a band structure, the vertical axis can be thought of as either "A" or "B", it doesn't matter.)
CAUTION 1: For all these quantities, physicists routinely and without explanation switch back and forth between discussing an electric potential (units of "volts") and discussing the energy involved in moving an electron across that potential (energy units). The conversion is 1V↔1eV (eV="electron-volt"=1.6×10-19 joules=23 kcal/mol).
CAUTION 2: The negative charge of an electron creates some confusion: Other things equal, electrons move to higher voltages but lower potential energies. For example, a semiconductor band diagram always uses an energy ("A") as the vertical axis, which means that if something shifts to a "more negative potential", it moves up in the band diagram.
CAUTION 3: Please notice that the words "voltage" and "electric potential difference" can mean either "A" or "C". In introductory physics courses, the electric field is in a vacuum, so "A" and "C" are the same, but if you read the definition in the textbook, the words "voltage" and "electric potential difference" are defined as "C" not "A". Yet in the real world, when "C" and "A" differ, the terms sometimes mean "A", because "A" is what you measure with a voltmeter. Anyway, both definitions are quite common, and you need to figure it out from context and experience.
CAUTION 4: The term "vacuum level" is very commonly used by semiconductor physicists, but is a tricky concept, I think trickier than some people realize. Without getting into details, I'll just say that in a popular but imperfect approximation, the difference in vacuum level between two points equals the difference in "C" times -1.
CAUTION 5: "Band-bending" is a term that comes from semiconductor band diagrams. When the bands slope upward or downward in a homogeneous solid, that means "C" is changing as a function of position.
Addendum: Conduction band, valence band, and quasi fermi level (a.k.a. imref):
Chemists are completely comfortable with the idea that different species can have different electrochemical potentials. For example, there is an electrochemical potential for H+, and a different electrochemical potential for Li+. In semiconductors, it is almost always appropriate to treat the "group of electrons in the conduction band" as one "species" with one electrochemical potential, and the "group of electrons in the valence band" as a different "species" with a different electrochemical potential.
Semiconductor physicists have a special terminology for this: They would say "there is a quasi-fermi level for electrons, and a quasi-fermi level for holes".
For example: When the electrochemical potential of electrons in the conduction band is higher than the electrochemical potential of electrons in the valence band in the same location, then there is a tendency for electrons to switch from the conduction band to the valence band. In the absence of other processes, the electrons will keep doing that until the electrochemical potential of the conduction and valence band is equal.
A semiconductor physicist would say that same sentences using different words, and a different mental image: When the quasi fermi level for electrons is higher than the quasi fermi level for holes in the same location, then there is a tendency for electrons and holes to recombine with each other. In the absence of other processes, the electrons and holes will keep recombining until the two quasi-fermi levels become equal to each other.
If you prefer a table:
| Abbreviated summary for semiconductors with split quasi fermi levels | ||
| Concept | What electrochemists call it | What semiconductor physicists call it |
| Total chemical potential of conduction-band electrons | "Electrochemical potential of conduction-band electrons" | "Electron quasi fermi level" or "Electron imref" |
| Total chemical potential of valence-band electrons | "Electrochemical potential of valence-band electrons" | "Hole quasi fermi level" or "Hole imref" |
| Internal chemical potential of conduction-band electrons | "Chemical potential of conduction-band electrons" | "Electron quasi fermi level, relative to vacuum", etc. |
| Internal chemical potential of valence-band electrons | "Chemical potential of valence-band electrons" | "Hole quasi fermi level, relative to vacuum", etc. |
| Electric potential | "Galvani potential" | "Electric potential", "Voltage", "Band-bending" (sort of), "Difference in vacuum level" (sort of) |
When the electron quasi fermi level is exactly equal to the hole quasi fermi level, then this value is called the "fermi level". If they are not equal, the semiconductor has no fermi level.
† Note: The textbook by Ashcroft and Mermin accidentally switches the terms "chemical potential" and "electrochemical potential" when discussion p-n junctions.
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