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It has seemed a good idea to replace the former re-direct page with a page that explained some of the basic facts about how the concept of Fermi level is used in electric engineering and semiconductor physics. There is a lot of confusion, both in textbooks and on Wikepedia, about the distinction between "Fermi level" and "Fermi energy" ( RGForbes ( talk) 03:09, 23 March 2009 (UTC))
This is a page about the
electrochemical potential of electrons. It should be made into a section of that page. --
Steve (
talk) 17:06, 27 March 2009 (UTC) Never mind, that's a silly idea, there's plenty to be said about electrons in particular, to warrent a dedicated article. :-) --
Steve (
talk)
06:58, 29 March 2009 (UTC)
The page says that it's "incorrect" to say that Fermi level and Fermi energy have the same definition. But lots of semiconductor-physics textbooks and reliable sources specifically state and use that definition. A definition can't be right or wrong, it can only be conventional or unconventional. There's no basis for saying that the definition used by one large group of well-regarded physicists is "correct" and the definition used by a different large group of well-regarded physicists (i.e. semiconductor physicists) is "incorrect". We should replace the term "correct" with "most common" and the term "incorrect" with "less common" or "specific to semiconductor physics" or something like that. -- Steve ( talk) 17:06, 27 March 2009 (UTC)
Article claims:
"Difference in voltage between conductor A and Earth = − (Difference in Fermi level between conductor A and Earth) / e"
This is false, because it neglects possible chemical potential differences. For example, solder an aluminum wire to a copper wire and put them on a table. The Fermi level will equilibrate between the two. But the voltage will not be the same, because of the volta potential at the junction arising from their different work functions. The word "voltage" has to be replaced with " electrochemical potential". -- Steve ( talk) 02:17, 29 March 2009 (UTC)
I didn't read the definitions very attentively, but it should be mentionned explicitly that in solid-state physics, the Fermi energy is defined as chemical potential as T → 0. The article should reflect this usage over others (which should be at chemical potential). Headbomb { ταλκ κοντριβς – WP Physics} 07:12, 29 March 2009 (UTC)
Yes I agree, however to introduce the Fermi level, you need to talk about the chemical potential first. As for the ref, I do have it (Ashcroft/Mermin Solid State Physics 1976, and possibly C. Kittel 6th edition), but I don't have it at hand. I'll pick it up tomorrow and I'll quote the relevant passages. But to ease your mind, the Fermi level represents the highest level occupied by an electron when in the system is in the lowest energy possible. You'll see that in metals both coincide when T--> 0K. In intrinsic semiconductors/insulators, the chemical potential is right smack in the middle of the gap when T -->0, but the Fermi level is at top of the conduction band. In extrinsic semiconductors, I forget where μ is (probably middle of the band, shifted towards donors/acceptors) the Fermi level will coindice with the donors level. It does not move, ever.
What is of use is the chemical potential, which is often called Fermi level because it is ridiculously close to the chemical potention in metals, which were historically "easier" to tackle. The fermi level concept first made its apparition in the drude model and sommerfeld model, well before the Bloch's band theory ever got around, where distinguishing between the chem pot and fermi energy introduces an error which is a fraction of kT (0.026eV at room temp [might have one more zero], which is quite negligeable). Then, when semiconductors/insulators got around, it became a serious error to refer to the chemical potential as the fermi level (at low temperatures), but not so much at room temp, where the FD distribution regains its Maxwell-Boltzmann-like characteristics. So people used both terms interchangeably anyway, as most people worked at RT, and people understood what was meant when they moved to low temps. And so began the huge mess of solid state physics.
So I'm sorta structuring the article into "Rigourous definition of chem pot/fermi energy" "Why it got confused (which becomes clear when you know the rigourous definitions)" and then the "meat" can be tackled. The important quantity is the chem pot, which is often, but wrongly, called the fermi energy. So basically, when people speak about the Fermi level/energy above T = 0, make the switch EF --> μ and then you have what people actually mean. I've spent two of my three master's seminaries dealing very directly with the fermi level [and I dealt with it in my third one as well] and related concepts so I'm quite familiar with it. Headbomb { ταλκ κοντριβς – WP Physics} 09:55, 3 April 2009 (UTC)
That's the thing. The Fermi level and the chem potential are NOT synonymous. EF is the energy of the most energetic electron when the system is its lowest energy configuration.
Take the simple case of a free electron gas [neglect states due to spin] contained in a cubic box of side L. You have
where
If you have N electrons, the lower energy configuration allowed is a sphere of radius
This defines the Fermi energy
and the equation
defines the Fermi surface [of a free electron gas]. It also defines the Fermi temperature
Now the chem potential is defined as the value that adjust the FD distribution so you have the following condition on f(E)
In our case (free electron model), the density of levels is
At T = 0, the electrons are all in a sphere of radius , i.e
But if and 0 otherwise. So in this case .
However, f(E) changes as T increases. The and the condition\
does not yield the same result for , is shifted to slightly lower energies. In the free electron model, the chemical potential is given by
In this case, at RT, the difference between the two is about 0.01%. Which is utterly negligible unless you go to temperature comparable to the Fermi temperature (~105K). This is why Fermi energy/chem potential have been used interchangeably. This behaviour (where EF and μ are comparable) is not applicable to materials in general, especially in the case of extrinsic semiconductors at low temperatures. The concept of the Fermi energy as "the energy of the most energetic electron when the system is in its lowest energy level" is ill-adapted for non-metals, as the useful quantity (chemical potential) always lies somewhere in the bandgap, and it therefore cannot correspond to the energy of any electron (even in the T=0 case). So instead, the Fermi energy is defined as the limit of the chemical potential when T = 0. This reproduces the usual definition of the "energy of the most energetic electron when the system is in its lowest energy configuration" when working with metals, but also yields a useful quantity when working with non-metals. See Ashcroft/Mermin Solid State Physics p.32-49 for a probably clearer explanation of all this.
A relevant quote from the book would be
“ | We shall se shortly that for metals the chemical potential remains equal to the Fermi energy to a high degree of precision, all the way up to room temperature. As a result, people frequently fail to make any distinction between the two when dealing with metals. This, however, can be dangerously misleading. In precise calculations it is essential to keep track of the extent to which μ, the chemical potential, differs from its zero temperature value, EF. | ” |
on page 43. [Yesterday's post sometimes conflated the Fermi energy definitions in terms of highest electron energy when the system is in its lowest energy config with μ when T=0 definition, apologies]. Headbomb { ταλκ κοντριβς – WP Physics} 04:44, 4 April 2009 (UTC)
Undo for now. However, the Fermi level is defined relative to EF (as the limit of μ→0) and not as μ. μ is the chemical potential, the the Fermi level, although both are sometimes used interchangeably. EF is the Fermi level/energy. Headbomb { ταλκ κοντριβς – WP Physics} 05:49, 6 April 2009 (UTC)
Right now (2010-09-09), there is no definition of EF in the section "Conduction band referencing and the parameter ζ" or the section "Earth-based referencing and the parameter µ". EF doesn't get "defined" until the section ""Fermi level" in semiconductor physics," and there it is not really defined. It seems to me that for a section entitled "Fermi Level" the variable that corresponds to it should be defined early and clearly. Since I don't fully follow all of these discussions here about definitions of Fermi levels, would one of you all please make this correction? Orange1111 ( talk) 06:43, 9 September 2010 (UTC)
Whether we like it or not, the term "voltage difference" is very very commonly used to denote purely the electrostatic potential difference between two points. Remember, V (the quantity whose gradient is E) is usually called "voltage", so a difference between two values of V is called "voltage difference". I think it's unhelpful to say this ubiquitous terminology is "wrong", better to address directly what it is and what it means.
The article addresses internal vs. external chemical potentials, but says "There is, however, no method of measuring these components separately." This isn't true. It's not easy to measure, but it's sure possible, and people do it all the time (through IV curve modeling, photoemission, kelvin probes, etc.) Let's remember that the electrostatic potential difference is a perfectly well-defined quantity: There's a physical E-field everywhere, and you can line integral to get an electrostatic potential difference. In principle, there's no conceptual problem at all: All three quantities (internal chemical potential, external chemical potential, total chemical potential) are well-defined and uniquely defined (other than what you call "zero"). It's just a matter of coming up with an appropriate method to tease them out. Agree? -- Steve ( talk) 08:52, 3 April 2009 (UTC)
This formula is only true if you make certain assumptions about what the density of states is. It's a correct series expansion if you have a free electron gas, but can be way off in a metal with funny density of states, as plenty of metals do. I think it would be best to just leave it out, but if the assumptions were clearly stated that would also be OK. Agreed? :-) -- Steve ( talk) 08:58, 3 April 2009 (UTC)
(unindent) g(E) doesn't have to be analytic everywhere, only about E = μ because you're taking the Taylor expansion of g(E) about E = μ. Additional requirement (because this does not only involve the Taylor expansion) is that g(E) vanishes as → −∞ and does not diverge faster than some power of E at E → +∞. Using a g(E) ~ E1⁄2, gives the above formula, yes. Headbomb { ταλκ κοντριβς – WP Physics} 19:42, 4 April 2009 (UTC)
A funny, seemingly-incorrect claim in the article: "In semiconductor physics it is conventional to work mainly with unreferenced energy symbols. This is possible because the relevant formulae of semiconductor physics mostly contain differences in energy levels, for example (EC-EF). Thus, for developing the basic theory of semiconductors there is little merit in introducing an absolute energy reference zero."
Mostly? My contention is that in all of condensed-matter physics, there is no situation where you need to discuss an absolute energy: Energy differences are the only things that will ever enter any formula. Can anyone come up with a counterexample? :-) -- Steve ( talk) 09:08, 3 April 2009 (UTC)
How would people feel about changing the presentation of the sections:
Instead, I propose we:
Would other people agree that this is a better way to lay out the information? :-) -- Steve ( talk) 09:26, 3 April 2009 (UTC)
I'd agree that the place to start is the non-interacting system, where most of the ideas you need to develop can be presented in mathematical rigor. It would be well to make the intro clearly separate this discussion from the interacting case. Then the quasi-particle formulation could be dealt with. Then the complexities of real systems could be brought up, and ramifications for the electrochemical potential and work function. That is a lot to do, and I'd guess the last part is where most of the present article is situated, without adequate attention to the independent particle foundations, where much of the present discussion would be unnecessary. Brews ohare ( talk) 12:46, 6 April 2009 (UTC)
I don't recall ever seeing the definition of Fermi level as the "state" that is given in the first sentence of the article, "In thermodynamics and solid-state physics, the Fermi level is the most energetic state occupied by an electron when the system is in the lowest energy configuration (i.e. at absolute zero)." I only recall seeing Fermi level defined as the energy of the top most filled state (Intro to Sol St Phys, Kittel) or as the chemical potential (Prin of Mod Phys, Leighton; Semicon Stat, Blakemore). Although these definitions of Kittel, Leighton, and Blakemore are inconsistent, they are consistent in defining Fermi level as an energy, not a state.
Can anyone give a source that says that the Fermi level is the "state", rather than the energy of the state? Otherwise we should change it to energy, which would make it the same Wikipedia definition as Fermi energy.
Also, it seems that some work is needed to coordinate or combine the articles Chemical potential, Electrochemical potential, Fermi level, and Fermi energy, at least to make them consistent in their definitions. -- Bob K31416 ( talk) 15:09, 6 April 2009 (UTC)
Concept | What chemists call it | What solid-state physicists call it | What semiconductor physicists call it | Current locale | Steve's ideal locale |
---|---|---|---|---|---|
Total chemical potential of electrons | Electrochemical potential of electrons | Chemical potential of electrons | Fermi level or Fermi energy | Chemical potential, Fermi level | Fermi level (plus a short description and "main article" link in chemical potential) |
Internal chemical potential of electrons | Chemical potential of electrons | Electrochemical potential of electrons | No name ("Fermi level relative to vacuum / conduction-band-minimum / etc.") | Little bits of Fermi level and Fermi energy, A section of Chemical potential | Maybe Work function, although they're only approximately the same... |
Internal chemical potential of electrons at 0K | N/A | Fermi energy (common), Fermi level (rare) | "Fermi level at zero kelvin" or something like that | Fermi energy and Fermi level, (redundantly) | Just Fermi energy |
Total chemical potential of non-electrons | Electrochemical potential | Chemical potential | N/A | Chemical potential and Electrochemical potential | Just Chemical potential |
Internal chemical potential of non-electrons | Chemical potential | Electrochemical potential | N/A | A section of chemical potential | A section of chemical potential |
I vote for reducing the electrochemical potential article down to a short discussion of terminology and a link to the chemical potential article, which already covers the exact same concept. Headbomb, since you're opposed to using "Fermi level" as the article-title for the concept in first row (total chemical potential of electrons), what do you propose instead? Chemical potential is already taken. Total chemical potential of electrons is awkward. Chemical potential of electrons is ambiguous. Any better ideas? -- Steve ( talk) 02:49, 7 April 2009 (UTC)
The table above is nonsense without being properly sourced. It is also nonsense, period, as its sources, even if listed, are highly suspect. The care in definition depends on the quality of the source. Fermi Energy/Fermi Level is not a concept from electrochemistry, it is a concept from physics. Electrochemists have a long historical tendency for perverting physics terminology, and that is the main problem here.
Kittel is purely an introductory text. You can find the more rigorous definition, and more thorough historical context, in Ashcroft and Mermin, or other references that actually delineate the history. This article concerns the Fermi level, not the chemical potential and all its interpretations (which go well beyond practical electrochemistry). Therefore, the article should stick to the mission at hand - rigourous/reliable definition of the "Fermi Level." — Preceding unsigned comment added by Wikibearwithme ( talk • contribs) 20:22, 28 May 2016 (UTC)
In chemistry, the symbol μ is very widely used for partial molar energy (measured in J/mol), and is being used in the present context for the related quantity measured in eV; μ is usually called "chemical potential". If we are going to use the term "chemical potential" as the basis for discussion, then we should define it clearly, and ideally we should give a definition that is capable of being carried out in the real world to give a specific number. The definition should probably take a form something like: μ is the work needed to place an electron at the Fermi level, starting from a state in which the electron is ******(in some specified initial state)****.
I have a problem in trying to formulate a definition of this kind for the quantity ζ0, because (in a free-electron model) the starting position has to be at the bottom of a Sommerfeld box (preferably not the one it is going to end up in). Also I cannot imagine any real-world process that could perform the transfer required. This is why I have doubts as to whether ζ0 really does correspond well to the quantity that the chemists call (electro-)chemical potential, (and is also why I do not use the symbol μ0 for Fermi energy). Sommerfeld, in his textbook on Thermodynamics and Statistical Mechanics, calls ζ the free enthalpy of an electron. The point is that, if we wish to start from definitions of the various contributions to chemical potential, then we will need to be careful (and probably lengthy) in our choice of words. The present article should probably be an introductory article about the usages of the term Fermi level, so it may be easier to start from the Fermi-Dirac distribution function, and put the considerations about components of chemical potential into a separate restructured article covering "chemical potential" and "electrochemical potential". ( RGForbes ( talk) 20:30, 9 April 2009 (UTC)) (Richard)
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We need to focus on what the sources say regarding the definition of Fermi level.
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help)Would anyone care to give any other sources and excerpts for the definition of Fermi level? My feeling is that we should define Fermi level as the chemical potential that appears in the above equation for the Fermi-Dirac distribution for a system of electrons. Thanks. -- Bob K31416 ( talk) 23:32, 9 April 2009 (UTC)
I changed the lead sentence of the article which defines Fermi level to define it as being a type of chemical potential for electrons in semiconductors. I gave a source for the definition. I only included semiconductors in the definition so far since I didn't have a source for metals. We can change the definition to include metals or anything else if there is a source to support those inclusions. I haven't made the corresponding changes yet in the rest of the article to allow time for discussion of this matter. Thanks. -- Bob K31416 ( talk) 17:22, 11 April 2009 (UTC)
There is a considerable amount of discussion in the article regarding energy referencing that seems to be editor original research without much substance. Does anyone know of any reliable sources for that information? If so, please give on this talk page the page numbers and excerpts from the sources that were used. Thanks. -- Bob K31416 ( talk) 15:05, 15 April 2009 (UTC)
In the lead sentence, I almost changed The Fermi level is an energy... to The Fermi level is an energy level..., but realized that would be a mistake. Energy level is an energy of a quantum state. For an intrinsic semiconductor, there are no states in the gap between the conduction and valence bands, yet there is a Fermi level there. -- Bob K31416 ( talk) 22:28, 17 April 2009 (UTC)
There is not "Fermi level" any more than a "Fermi energy" there; it is a convention of specifying/estimating the Fermi level as mid-gap (a probabolistic statement). Calling it one or the other does not make it any more rigorously defined or physically accurate.
Wikibearwithme (
talk)
20:04, 28 May 2016 (UTC)
Does anybody mind if this section is thrown away? It belongs rather to the Fermi level article. —Preceding unsigned comment added by Evgeny ( talk • contribs) 17:03, 7 May 2009 (UTC)
Perhaps a bit of bias on my part as I've been working on it a lot, but I upgraded this article to High importance (any semiconductor physics discussion involves Fermi level), and changed from start to C quality. -- Nanite ( talk) 23:40, 26 May 2013 (UTC)
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The article lead currently defines:
It is unclear what that 50% probability of occupation means. The Fermi level is used in semiconductor physics to explain semiconductor conductivity; there, the Fermi level lies in the band gap, where no valid energy levels exist for electrons to occupy. That seems more like a 0% probability to me ... -- MewTheEditor ( talk) 12:06, 8 February 2021 (UTC)
The article shows that the Fermi level for insulators lies within a gap. This statement seems to come out of nowhere. Is it confirmable that this mid-gap energy level has any physical relevance? Perhaps in ARPES?
Would this not imply that if one could apply only half the bandgap worth of voltage to a unit cell, the conduction band would start to fill up? Or how else is one to interpret the position of the Fermi-level in this case?
Lastly, denoting the Fermi-level as seems odd when the article otherwise implies that it is equivalent to the chemical potential, expressed typically by . From my experience the Fermi-energy (not the Fermi-level) is always denoted by and the chemical potential is always denoted by . There is discrepancies between authors what the Fermi-level is (either the Fermi-energy OR the chemical potential). However, in this article it is denoted both as AND . Isn't that confusing? 2001:9E8:899B:E700:244C:BDBB:38D9:9CE9 ( talk) 19:24, 27 February 2024 (UTC)
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||
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This is the
talk page for discussing improvements to the
Fermi level article. This is not a forum for general discussion of the article's subject. |
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Find sources: Google ( books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL |
It has seemed a good idea to replace the former re-direct page with a page that explained some of the basic facts about how the concept of Fermi level is used in electric engineering and semiconductor physics. There is a lot of confusion, both in textbooks and on Wikepedia, about the distinction between "Fermi level" and "Fermi energy" ( RGForbes ( talk) 03:09, 23 March 2009 (UTC))
This is a page about the
electrochemical potential of electrons. It should be made into a section of that page. --
Steve (
talk) 17:06, 27 March 2009 (UTC) Never mind, that's a silly idea, there's plenty to be said about electrons in particular, to warrent a dedicated article. :-) --
Steve (
talk)
06:58, 29 March 2009 (UTC)
The page says that it's "incorrect" to say that Fermi level and Fermi energy have the same definition. But lots of semiconductor-physics textbooks and reliable sources specifically state and use that definition. A definition can't be right or wrong, it can only be conventional or unconventional. There's no basis for saying that the definition used by one large group of well-regarded physicists is "correct" and the definition used by a different large group of well-regarded physicists (i.e. semiconductor physicists) is "incorrect". We should replace the term "correct" with "most common" and the term "incorrect" with "less common" or "specific to semiconductor physics" or something like that. -- Steve ( talk) 17:06, 27 March 2009 (UTC)
Article claims:
"Difference in voltage between conductor A and Earth = − (Difference in Fermi level between conductor A and Earth) / e"
This is false, because it neglects possible chemical potential differences. For example, solder an aluminum wire to a copper wire and put them on a table. The Fermi level will equilibrate between the two. But the voltage will not be the same, because of the volta potential at the junction arising from their different work functions. The word "voltage" has to be replaced with " electrochemical potential". -- Steve ( talk) 02:17, 29 March 2009 (UTC)
I didn't read the definitions very attentively, but it should be mentionned explicitly that in solid-state physics, the Fermi energy is defined as chemical potential as T → 0. The article should reflect this usage over others (which should be at chemical potential). Headbomb { ταλκ κοντριβς – WP Physics} 07:12, 29 March 2009 (UTC)
Yes I agree, however to introduce the Fermi level, you need to talk about the chemical potential first. As for the ref, I do have it (Ashcroft/Mermin Solid State Physics 1976, and possibly C. Kittel 6th edition), but I don't have it at hand. I'll pick it up tomorrow and I'll quote the relevant passages. But to ease your mind, the Fermi level represents the highest level occupied by an electron when in the system is in the lowest energy possible. You'll see that in metals both coincide when T--> 0K. In intrinsic semiconductors/insulators, the chemical potential is right smack in the middle of the gap when T -->0, but the Fermi level is at top of the conduction band. In extrinsic semiconductors, I forget where μ is (probably middle of the band, shifted towards donors/acceptors) the Fermi level will coindice with the donors level. It does not move, ever.
What is of use is the chemical potential, which is often called Fermi level because it is ridiculously close to the chemical potention in metals, which were historically "easier" to tackle. The fermi level concept first made its apparition in the drude model and sommerfeld model, well before the Bloch's band theory ever got around, where distinguishing between the chem pot and fermi energy introduces an error which is a fraction of kT (0.026eV at room temp [might have one more zero], which is quite negligeable). Then, when semiconductors/insulators got around, it became a serious error to refer to the chemical potential as the fermi level (at low temperatures), but not so much at room temp, where the FD distribution regains its Maxwell-Boltzmann-like characteristics. So people used both terms interchangeably anyway, as most people worked at RT, and people understood what was meant when they moved to low temps. And so began the huge mess of solid state physics.
So I'm sorta structuring the article into "Rigourous definition of chem pot/fermi energy" "Why it got confused (which becomes clear when you know the rigourous definitions)" and then the "meat" can be tackled. The important quantity is the chem pot, which is often, but wrongly, called the fermi energy. So basically, when people speak about the Fermi level/energy above T = 0, make the switch EF --> μ and then you have what people actually mean. I've spent two of my three master's seminaries dealing very directly with the fermi level [and I dealt with it in my third one as well] and related concepts so I'm quite familiar with it. Headbomb { ταλκ κοντριβς – WP Physics} 09:55, 3 April 2009 (UTC)
That's the thing. The Fermi level and the chem potential are NOT synonymous. EF is the energy of the most energetic electron when the system is its lowest energy configuration.
Take the simple case of a free electron gas [neglect states due to spin] contained in a cubic box of side L. You have
where
If you have N electrons, the lower energy configuration allowed is a sphere of radius
This defines the Fermi energy
and the equation
defines the Fermi surface [of a free electron gas]. It also defines the Fermi temperature
Now the chem potential is defined as the value that adjust the FD distribution so you have the following condition on f(E)
In our case (free electron model), the density of levels is
At T = 0, the electrons are all in a sphere of radius , i.e
But if and 0 otherwise. So in this case .
However, f(E) changes as T increases. The and the condition\
does not yield the same result for , is shifted to slightly lower energies. In the free electron model, the chemical potential is given by
In this case, at RT, the difference between the two is about 0.01%. Which is utterly negligible unless you go to temperature comparable to the Fermi temperature (~105K). This is why Fermi energy/chem potential have been used interchangeably. This behaviour (where EF and μ are comparable) is not applicable to materials in general, especially in the case of extrinsic semiconductors at low temperatures. The concept of the Fermi energy as "the energy of the most energetic electron when the system is in its lowest energy level" is ill-adapted for non-metals, as the useful quantity (chemical potential) always lies somewhere in the bandgap, and it therefore cannot correspond to the energy of any electron (even in the T=0 case). So instead, the Fermi energy is defined as the limit of the chemical potential when T = 0. This reproduces the usual definition of the "energy of the most energetic electron when the system is in its lowest energy configuration" when working with metals, but also yields a useful quantity when working with non-metals. See Ashcroft/Mermin Solid State Physics p.32-49 for a probably clearer explanation of all this.
A relevant quote from the book would be
“ | We shall se shortly that for metals the chemical potential remains equal to the Fermi energy to a high degree of precision, all the way up to room temperature. As a result, people frequently fail to make any distinction between the two when dealing with metals. This, however, can be dangerously misleading. In precise calculations it is essential to keep track of the extent to which μ, the chemical potential, differs from its zero temperature value, EF. | ” |
on page 43. [Yesterday's post sometimes conflated the Fermi energy definitions in terms of highest electron energy when the system is in its lowest energy config with μ when T=0 definition, apologies]. Headbomb { ταλκ κοντριβς – WP Physics} 04:44, 4 April 2009 (UTC)
Undo for now. However, the Fermi level is defined relative to EF (as the limit of μ→0) and not as μ. μ is the chemical potential, the the Fermi level, although both are sometimes used interchangeably. EF is the Fermi level/energy. Headbomb { ταλκ κοντριβς – WP Physics} 05:49, 6 April 2009 (UTC)
Right now (2010-09-09), there is no definition of EF in the section "Conduction band referencing and the parameter ζ" or the section "Earth-based referencing and the parameter µ". EF doesn't get "defined" until the section ""Fermi level" in semiconductor physics," and there it is not really defined. It seems to me that for a section entitled "Fermi Level" the variable that corresponds to it should be defined early and clearly. Since I don't fully follow all of these discussions here about definitions of Fermi levels, would one of you all please make this correction? Orange1111 ( talk) 06:43, 9 September 2010 (UTC)
Whether we like it or not, the term "voltage difference" is very very commonly used to denote purely the electrostatic potential difference between two points. Remember, V (the quantity whose gradient is E) is usually called "voltage", so a difference between two values of V is called "voltage difference". I think it's unhelpful to say this ubiquitous terminology is "wrong", better to address directly what it is and what it means.
The article addresses internal vs. external chemical potentials, but says "There is, however, no method of measuring these components separately." This isn't true. It's not easy to measure, but it's sure possible, and people do it all the time (through IV curve modeling, photoemission, kelvin probes, etc.) Let's remember that the electrostatic potential difference is a perfectly well-defined quantity: There's a physical E-field everywhere, and you can line integral to get an electrostatic potential difference. In principle, there's no conceptual problem at all: All three quantities (internal chemical potential, external chemical potential, total chemical potential) are well-defined and uniquely defined (other than what you call "zero"). It's just a matter of coming up with an appropriate method to tease them out. Agree? -- Steve ( talk) 08:52, 3 April 2009 (UTC)
This formula is only true if you make certain assumptions about what the density of states is. It's a correct series expansion if you have a free electron gas, but can be way off in a metal with funny density of states, as plenty of metals do. I think it would be best to just leave it out, but if the assumptions were clearly stated that would also be OK. Agreed? :-) -- Steve ( talk) 08:58, 3 April 2009 (UTC)
(unindent) g(E) doesn't have to be analytic everywhere, only about E = μ because you're taking the Taylor expansion of g(E) about E = μ. Additional requirement (because this does not only involve the Taylor expansion) is that g(E) vanishes as → −∞ and does not diverge faster than some power of E at E → +∞. Using a g(E) ~ E1⁄2, gives the above formula, yes. Headbomb { ταλκ κοντριβς – WP Physics} 19:42, 4 April 2009 (UTC)
A funny, seemingly-incorrect claim in the article: "In semiconductor physics it is conventional to work mainly with unreferenced energy symbols. This is possible because the relevant formulae of semiconductor physics mostly contain differences in energy levels, for example (EC-EF). Thus, for developing the basic theory of semiconductors there is little merit in introducing an absolute energy reference zero."
Mostly? My contention is that in all of condensed-matter physics, there is no situation where you need to discuss an absolute energy: Energy differences are the only things that will ever enter any formula. Can anyone come up with a counterexample? :-) -- Steve ( talk) 09:08, 3 April 2009 (UTC)
How would people feel about changing the presentation of the sections:
Instead, I propose we:
Would other people agree that this is a better way to lay out the information? :-) -- Steve ( talk) 09:26, 3 April 2009 (UTC)
I'd agree that the place to start is the non-interacting system, where most of the ideas you need to develop can be presented in mathematical rigor. It would be well to make the intro clearly separate this discussion from the interacting case. Then the quasi-particle formulation could be dealt with. Then the complexities of real systems could be brought up, and ramifications for the electrochemical potential and work function. That is a lot to do, and I'd guess the last part is where most of the present article is situated, without adequate attention to the independent particle foundations, where much of the present discussion would be unnecessary. Brews ohare ( talk) 12:46, 6 April 2009 (UTC)
I don't recall ever seeing the definition of Fermi level as the "state" that is given in the first sentence of the article, "In thermodynamics and solid-state physics, the Fermi level is the most energetic state occupied by an electron when the system is in the lowest energy configuration (i.e. at absolute zero)." I only recall seeing Fermi level defined as the energy of the top most filled state (Intro to Sol St Phys, Kittel) or as the chemical potential (Prin of Mod Phys, Leighton; Semicon Stat, Blakemore). Although these definitions of Kittel, Leighton, and Blakemore are inconsistent, they are consistent in defining Fermi level as an energy, not a state.
Can anyone give a source that says that the Fermi level is the "state", rather than the energy of the state? Otherwise we should change it to energy, which would make it the same Wikipedia definition as Fermi energy.
Also, it seems that some work is needed to coordinate or combine the articles Chemical potential, Electrochemical potential, Fermi level, and Fermi energy, at least to make them consistent in their definitions. -- Bob K31416 ( talk) 15:09, 6 April 2009 (UTC)
Concept | What chemists call it | What solid-state physicists call it | What semiconductor physicists call it | Current locale | Steve's ideal locale |
---|---|---|---|---|---|
Total chemical potential of electrons | Electrochemical potential of electrons | Chemical potential of electrons | Fermi level or Fermi energy | Chemical potential, Fermi level | Fermi level (plus a short description and "main article" link in chemical potential) |
Internal chemical potential of electrons | Chemical potential of electrons | Electrochemical potential of electrons | No name ("Fermi level relative to vacuum / conduction-band-minimum / etc.") | Little bits of Fermi level and Fermi energy, A section of Chemical potential | Maybe Work function, although they're only approximately the same... |
Internal chemical potential of electrons at 0K | N/A | Fermi energy (common), Fermi level (rare) | "Fermi level at zero kelvin" or something like that | Fermi energy and Fermi level, (redundantly) | Just Fermi energy |
Total chemical potential of non-electrons | Electrochemical potential | Chemical potential | N/A | Chemical potential and Electrochemical potential | Just Chemical potential |
Internal chemical potential of non-electrons | Chemical potential | Electrochemical potential | N/A | A section of chemical potential | A section of chemical potential |
I vote for reducing the electrochemical potential article down to a short discussion of terminology and a link to the chemical potential article, which already covers the exact same concept. Headbomb, since you're opposed to using "Fermi level" as the article-title for the concept in first row (total chemical potential of electrons), what do you propose instead? Chemical potential is already taken. Total chemical potential of electrons is awkward. Chemical potential of electrons is ambiguous. Any better ideas? -- Steve ( talk) 02:49, 7 April 2009 (UTC)
The table above is nonsense without being properly sourced. It is also nonsense, period, as its sources, even if listed, are highly suspect. The care in definition depends on the quality of the source. Fermi Energy/Fermi Level is not a concept from electrochemistry, it is a concept from physics. Electrochemists have a long historical tendency for perverting physics terminology, and that is the main problem here.
Kittel is purely an introductory text. You can find the more rigorous definition, and more thorough historical context, in Ashcroft and Mermin, or other references that actually delineate the history. This article concerns the Fermi level, not the chemical potential and all its interpretations (which go well beyond practical electrochemistry). Therefore, the article should stick to the mission at hand - rigourous/reliable definition of the "Fermi Level." — Preceding unsigned comment added by Wikibearwithme ( talk • contribs) 20:22, 28 May 2016 (UTC)
In chemistry, the symbol μ is very widely used for partial molar energy (measured in J/mol), and is being used in the present context for the related quantity measured in eV; μ is usually called "chemical potential". If we are going to use the term "chemical potential" as the basis for discussion, then we should define it clearly, and ideally we should give a definition that is capable of being carried out in the real world to give a specific number. The definition should probably take a form something like: μ is the work needed to place an electron at the Fermi level, starting from a state in which the electron is ******(in some specified initial state)****.
I have a problem in trying to formulate a definition of this kind for the quantity ζ0, because (in a free-electron model) the starting position has to be at the bottom of a Sommerfeld box (preferably not the one it is going to end up in). Also I cannot imagine any real-world process that could perform the transfer required. This is why I have doubts as to whether ζ0 really does correspond well to the quantity that the chemists call (electro-)chemical potential, (and is also why I do not use the symbol μ0 for Fermi energy). Sommerfeld, in his textbook on Thermodynamics and Statistical Mechanics, calls ζ the free enthalpy of an electron. The point is that, if we wish to start from definitions of the various contributions to chemical potential, then we will need to be careful (and probably lengthy) in our choice of words. The present article should probably be an introductory article about the usages of the term Fermi level, so it may be easier to start from the Fermi-Dirac distribution function, and put the considerations about components of chemical potential into a separate restructured article covering "chemical potential" and "electrochemical potential". ( RGForbes ( talk) 20:30, 9 April 2009 (UTC)) (Richard)
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We need to focus on what the sources say regarding the definition of Fermi level.
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help)Would anyone care to give any other sources and excerpts for the definition of Fermi level? My feeling is that we should define Fermi level as the chemical potential that appears in the above equation for the Fermi-Dirac distribution for a system of electrons. Thanks. -- Bob K31416 ( talk) 23:32, 9 April 2009 (UTC)
I changed the lead sentence of the article which defines Fermi level to define it as being a type of chemical potential for electrons in semiconductors. I gave a source for the definition. I only included semiconductors in the definition so far since I didn't have a source for metals. We can change the definition to include metals or anything else if there is a source to support those inclusions. I haven't made the corresponding changes yet in the rest of the article to allow time for discussion of this matter. Thanks. -- Bob K31416 ( talk) 17:22, 11 April 2009 (UTC)
There is a considerable amount of discussion in the article regarding energy referencing that seems to be editor original research without much substance. Does anyone know of any reliable sources for that information? If so, please give on this talk page the page numbers and excerpts from the sources that were used. Thanks. -- Bob K31416 ( talk) 15:05, 15 April 2009 (UTC)
In the lead sentence, I almost changed The Fermi level is an energy... to The Fermi level is an energy level..., but realized that would be a mistake. Energy level is an energy of a quantum state. For an intrinsic semiconductor, there are no states in the gap between the conduction and valence bands, yet there is a Fermi level there. -- Bob K31416 ( talk) 22:28, 17 April 2009 (UTC)
There is not "Fermi level" any more than a "Fermi energy" there; it is a convention of specifying/estimating the Fermi level as mid-gap (a probabolistic statement). Calling it one or the other does not make it any more rigorously defined or physically accurate.
Wikibearwithme (
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Does anybody mind if this section is thrown away? It belongs rather to the Fermi level article. —Preceding unsigned comment added by Evgeny ( talk • contribs) 17:03, 7 May 2009 (UTC)
Perhaps a bit of bias on my part as I've been working on it a lot, but I upgraded this article to High importance (any semiconductor physics discussion involves Fermi level), and changed from start to C quality. -- Nanite ( talk) 23:40, 26 May 2013 (UTC)
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The article lead currently defines:
It is unclear what that 50% probability of occupation means. The Fermi level is used in semiconductor physics to explain semiconductor conductivity; there, the Fermi level lies in the band gap, where no valid energy levels exist for electrons to occupy. That seems more like a 0% probability to me ... -- MewTheEditor ( talk) 12:06, 8 February 2021 (UTC)
The article shows that the Fermi level for insulators lies within a gap. This statement seems to come out of nowhere. Is it confirmable that this mid-gap energy level has any physical relevance? Perhaps in ARPES?
Would this not imply that if one could apply only half the bandgap worth of voltage to a unit cell, the conduction band would start to fill up? Or how else is one to interpret the position of the Fermi-level in this case?
Lastly, denoting the Fermi-level as seems odd when the article otherwise implies that it is equivalent to the chemical potential, expressed typically by . From my experience the Fermi-energy (not the Fermi-level) is always denoted by and the chemical potential is always denoted by . There is discrepancies between authors what the Fermi-level is (either the Fermi-energy OR the chemical potential). However, in this article it is denoted both as AND . Isn't that confusing? 2001:9E8:899B:E700:244C:BDBB:38D9:9CE9 ( talk) 19:24, 27 February 2024 (UTC)