|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.
CAUTION 6: I'm sick of hearing people accuse each other of misunderstanding a concept, when actually they both understand it but with different terminologies. For example, the fact that semiconductor physicists often use "Fermi energy" to mean "Fermi level" does not mean that semiconductor physicists don't understand that the Fermi level changes with temperature. It's like if an American said "Australians don't even know the difference between soccer and football"!
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