Talk:Electron hole

Minor Clarification

The electron hole is not the mathematical opposite of the electron. The mathematical opposite of an electron is the positron; and it was predicted by Paul Dirac when he formulated the relativistic form of quantum mechanics. The Dirac Equation has two solutions; the first represents the negatively charged electron and the second, the positively charged positron. The electron hole model is a simplistic way of modeling (looking at) the absence of an electron at atomic level. It can be used in the shell model for atoms and also in the band structure for crystalline materials and quasi-crystals, also in materials such as glasses. The hole model has also been used in nuclear pysics, when the nucleus is modelled by the nuclear shell model. The major problem with the hole concept is that it violates the basic nature of quantum mechanics for a many body system. The wave function for the entire system must be symmetric (or anti-symmetric) in order to satisfy the principle that particles are identical and cannot be distinguished from each other. Collective motion of electrons and other quantum particles must always be considered. The mathematics of a many body problem is very complex and numerical analysis is usually carried out using computer-aided calculatons While the hole model does provide fairly good engineering results for calculations, however one must keep in mind that it will breakdown in many cases and give incorrect results, especially in transitions between different quantum (or excited)states. Wiseoldowl 05:25, 29 October 2007 (UTC)

Unfortunately, while this explantion is taught in enginnering schools it has a major problem. Specifically, it violates conservation of charge. That it does can be shown by the Hall Effect.

In short, the electron gets promoted and "leaves a hole behind". Then, presto chango, this hole "acquires" a positive charge that can be detected by the hall effect. The hall effect is detecting something, no doubt about that. But that "something" is definitely not a "hole" or a lack of electron. Its something with a charge moving with a velocity.

Does anyone *really* know how this stuff works?

"Its something with a charge moving with a velocity". No, its a hole that moves into the contact with which you measure current/resistance/whatever, aka an electron moving out of the contact.

---

The positive charge comes from the nuclei in the crystal lattice. The lattice is initially neutral:

                                 -               -                    
    +             +               +            +               +
   -              -                                           -

then an electron is dislodged from a site, leaving a localised negative charge at one location and a localised positive charge at another

                                                -                    
    +             +               +            +               +
   -              -                            -              -

The localised positive charge is the "hole", and it moves when the electrons near it move in the opposite direction. Here the hole moves left:

                                                -                    
    +             +               +            +               +
   -                    -                      -              -

                                  -             -                    
    +             +               +            +               +
   -                                           -              -

A hole is in some sense imaginary, it just consists of an excess of protons compared to electrons. But it turns out that to describe this excess as a particle with mass and velocity is very useful theoretically. -- Tim Starling 23:39, Feb 3, 2004 (UTC)

I've added a mention of the positive charges which are "unmasked" when a hole sits on a previously neutral atom. In the movie theater, the humans have negative charge, the seats are positive, and a filled seat is neutral while a vacant seat is positive.--Wjbeaty 07:05, August 7, 2005 (UTC)

---

Do holes repel each other? If they really behave like particles they would. For instance, a metal sphere with a few electrons missing will apparently have all of its charge (positive) migrate to the surface of the sphere and evenly distribute itself. This is confusing to me, though, since the electrons are repelling each other. I would expect them to spread out as far as possible, even if there are less electrons than protons. This could be seen as holes spreading out as far as possible, but they are not real particles, and it is not obvious how they would repel each other. Can someone explain this and include some type of explanation in the article?

In a neutral conductor, all the electrons are next to protons which cancel them out in the long run, so electrons in a conductor don't normally repel each other. And if you have some neutral p-type semiconductor, then all the holes are near negative dopant ions, so the holes don't repel each other either. (Remember, when the holes first left the neutral dopant atoms, the dopant atoms acquired an extra electron and became negative.) Now if you put a positive charge on a piece of p-type semiconductor, so there are now more holes than there are negative dopant ions, in that case the extra uncancelled holes will spew e-fields out to infinity. They will affect all the electrons in the material. If two of these uncancelled holes are near each other, they will more strongly attract the adjacent electrons which *aren't* between the holes. (Notice that those particular electrons each see two holes in the same general direction. An electron which finds itself between two holes doesn't see this.) These outside-neighboring electrons fall into their nearby holes, and so the holes have moved apart. The process can continue until the holes are spread out equally and the forces on all the neighboring electrons are balanced, so the holes stop moving. --Wjbeaty 07:05, August 7, 2005 (UTC)

Likewise, in semiconductor thermoelectricity, it makes sense that excess electrons would diffuse from a hotter region to a colder region, because of their thermal energy, but it is not as obvious why holes (in a p-type semiconductor) would migrate away from the hot region. But they do. (I think.) - Omegatron 13:49, Apr 6, 2004 (UTC)

Do electrons diffuse that way? Or do they simply diffuse, period, and the more they wiggle, the faster they diffuse? With holes, the more their neighboring electrons wiggle, the more those electrons would tend to jump into the hole, causing it to move. --Wjbeaty 07:05, August 7, 2005 (UTC)

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This material was added to a duplicate page. Is any of it useful here?

Hole is a quantum-mechanical counterpart of an electron. It arises out of the solution of Schrodinger's equation for a periodic potential, which exists inside a semiconductor crystal. One can think it as a 'fictitious' particle or just 'an absence of electron' which is able to carry the current in a semiconducotr just in opposite direction to that of electron current. Quantum-mechanical considerations show that though it behaves just like a positively charged electron, its mass is little higher than that of an electron and consequently it has lower mobility. Naturally, devices where holes are majority carriers, is slower in operation than the devices having electron as majority carriers.

The important thing to remember is that a hole is not a positron, which is a fundamental particle having exactly same features as electron but opposite charge.

Rmhermen 21:19, Jul 16, 2004 (UTC)

Congrats!

I must congratulate whoever wrote the chair hopping analogy into this article, it makes it the easiest of all the subatomic particle related articles to understand, despite it's harsh concept! Thanks! --Quadraxis 02:28, 9 November 2005 (UTC)

I came here specifically to write what Quadraxis wrote. The analogy is beautiful. I wasn't sure I understood hole migration but now I know I did understand it after all. Hooray. --Anonymous 22 November 2005

Semiconductor spelling...

• Add me to the list of those who came here specifically to praise that analogy. Nice work! uFu 20:17, 1 January 2007 (UTC)

Same :D--Totophe64 15:21, 13 March 2007 (UTC)

I agree that the anology makes easy reading and provides an easy to follow explanation, but could we somehow format the analogy (indented, italicised?) so that it is very clear that this is an analogy alongside a scientific definition of a hole? Surely an encyclopedia should not seek to define things by analogy? --Drown 12:48, 12 May 2007 (UTC)

Hi, I found this analogy very good. I like to be able to quote this in the essay on photocatalysis that I am writing, though I'm not sure who the author is. -eugene_lai

To put it simply...

Can't we just say that an electron hole is the absence of an electron from an atom full stop?--67.10.200.101 03:22, 17 November 2006 (UTC)

I agree, this article needs an accessible introductory sentence. How about adding this as an introductory paragraph?

"An electron hole is a mathematical concept describing the lack of an electron. Semiconductor physics treats holes as charge carriers, though there is no such particle that physically exists. It is different from the positron, which is the antimatter duplicate of the electron, identical to the electron except for its positive charge."

--205.201.141.146 20:17, 3 April 2007 (UTC)

There seems to be a lot of misunderstanding about the difference between a vacancy and a hole.

• A vacancy is a 'lack of an electron' (specifically an unoccupied state in the reciprocal lattice).
• An electron hole is a concept representing a vacancy as a positive charge carrier in an inverted potential.

Unfortunately there is no simple, correct way to put this. The theatre seating analogy is a nice introduction to the concept, but can only be taken so far.

--DJIndica 21:34, 29 May 2007 (UTC)

comment deleted

(See also the section in the article called "A hole is the absence of a negative-mass electron".)

I don't personally see this article as being unusually / egregiously confusing. Of course it has room for improvement (as everything does), but I think it warrants minor not major changes. But maybe I'm missing something! So would you mind spelling out in more detail how you find the article confusing and how you might imagine improving it? Thanks, --Steve (talk) 13:50, 16 April 2018 (UTC)

comment deleted

Quote from the article: "A hole near the top of the valence band moves the same way as an electron near the top of the valence band would move (which is in the opposite direction compared to conduction-band electrons experiencing the same force.)...This is an example where the auditorium analogy above is misleading. When a person moves left in a full auditorium, an empty seat moves right. But in this section we are imagining how electrons move through k-space, not real space, and the effect of a force is to move all the electrons through k-space in the same direction at the same time. In this context, a better analogy is a bubble underwater in a river: The bubble moves the same direction as the water, not opposite." Does that help? --Steve (talk) 16:04, 16 April 2018 (UTC)

What the river is trying to describe is this:

-E-> ------+-----

-E-> -------+----

-E-> --------+---

All electrons move to the right, while a free electron would move to the left. The "free space" moves with the electrons.

Makes sense to me now. I will delete earlier comments to avoid confusion. Thanks.

Negative charge?

I'm looking at the pic of the helium atom, and the caption says that when an electron leaves its shell, then the atom gets a negative charge. Last time I checked, the opposite is true. Any comments? Ghostwo 23:51, 16 October 2007 (UTC)

Minimal fix implemented. Archelon 03:01, 22 October 2007 (UTC)

Rename?

A discussion has been started at Wikipedia talk:WikiProject Physics#Electron hole concerning the proper title for this article, currently Electron hole. Mooted so far have been: Hole (solid state physics), Hole (charge carrier), Hole (quasiparticle), Hole (physics and chemistry), and Hole (semiconductors). Presumably the section on quantum chemistry would remain at this title through any move, as it would not be appropriate under any of the others.

• Hole (quasiparticle) or Hole (solid state physics) would be my preference, though any (including the current title) would not be so bad. - Eldereft (cont.) 01:23, 31 December 2008 (UTC)

I say keep it as it is. "Electron hole" is pretty common in textbooks. See [1]. The textbooks I've read typically call it an "electron hole" when it's first introduced, then they say it's universally abbreviated "hole", and call it "hole" for the rest of the book. We should do the same: Title the article "electron hole", explain in the first sentence that everyone abbreviates it "hole", and call it "hole" for the rest of the article. --Steve (talk) 01:48, 31 December 2008 (UTC)

I think Steve made some good points but the part, "then they say it's universally abbreviated 'hole', and call it 'hole' for the rest of the book" seems to be a strong argument in favor of Hole for the title, with an appropriate disambiguation in parentheses. It seems better to call it hole, beginning with the title. Personally, when I see Electron hole for the title, what first jumps into my mind is that recombination should be at the end of it.

Also, a way to misinterpret the title Electron hole is to think that it is a hole that contains electrons, which is the opposite of what it is supposed to mean. Of course in context, electron hole wouldn't be misinterpreted, but as a title it is not yet in context when someone reads it. In fact, one of the functions of a title is to set the context, which I think would be better achieved with Hole and a disambiguation.

Here's another candidate to add to the list, Hole (vacant electron state). Of the new ones considered so far, I haven't decided which one I like best. --Bob K31416 (talk) 04:31, 31 December 2008 (UTC)

There are plenty of cases where the most "official" name differs from the most common name, and I can think of plenty of wikipedia articles that take either one as the title. In addition to electron hole, I'm also fond of Hole (quasiparticle), as a close second or maybe even first. All the other possibilities raised so far are much worse, in my mind, for one reason or another. :-) --Steve (talk) 16:50, 31 December 2008 (UTC)

Re "There are plenty of cases where the most "official" name differs from the most common name..." - For me at least, "electron hole" is neither official nor more common than "hole".

BTW I wonder what the folks who use the term "electron hole" do when they talk about the recombination of an electron and an "electron hole". Do they call it electron-electron hole recombination? --Bob K31416 (talk) 00:30, 1 January 2009 (UTC)

I've definitely seen this sentiment if not this exact usage in discussion on dye-sensitised solar cells, wherein the electrolyte is considered a hole-transport medium and recombination is a potential problem if the dye is not reduced fast enough. Eutactic (talk) 03:34, 9 July 2010 (UTC)

I've never cared much for the term "hole". I understand it's usefulness in explaining valence interactions to the non scientifically inclined, as I've seen the term in many electronics textbooks. But, I've never seen the term used in actual scientific literature. There should be some distinction explaining that a hole is merely a vacancy in the valance shell; that it serves no actual useful purpose and that it is not a particle. I've found that people who learn "hole" first also have issues with understanding chemistry properly (I've been a tutor).I'd like to move that all mentioning of the term should be done so with improved clarity. Pimpachu (talk) 03:42, 17 August 2009 (UTC) P.S. I like quasi-particle and vacant electron state for rename.

E-holes and LEDs

For the physicist wannabes among us, could you please add something about how electron holes (or whatever you eventually decide to call them) make LEDs work? They figure prominently, but at the same time obscurely, in the wiki article I read on LEDs a while ago. And what would be really, really useful, is to compare with ordinary electric conduction (what I learned many years ago sounds exactly like the empty chair analogy). — Preceding unsigned comment added by 78.228.108.6 (talk) 08:30, 19 June 2011 (UTC)

Note

Basically current carried by valence electrons in valence band is said to be the hole current and current carried by free electrons (known as conduction electrons) in conduction band is termed as electron current.. — Preceding unsigned comment added by VIV0411 (talk • contribs) 01:41, 12 August 2011 (UTC)

Shortcomings of auditorium (or parking lot) analogy

The article prominently features the analogy where an empty seat in an auditorium moves left as one person after another moves to the right. (I've also seen the same thing with an empty space in an almost-full parking lot.) This is intuitively appealing, and worth discussing, but ultimately misleading. If you take it literally, you get the wrong prediction for the sign of the Hall effect for p-type materials. (Also wrong sign for Seebeck effect, etc.)

The missing ingredient is the curvature of the valence band: Electrons near the top of the valence band behave like they have a negative mass, because the band curves down instead of up. So for example, if an electromagnetic force pushes a valence-band-maximum electron to the right, the electron actually moves left in response. The holes inherit this funny behavior from the electrons.

See my detailed explanation on a different website. I would add something like that here (in addition to the auditorium analogy), but I'd like to find a citation first...anyone seen an explanation along these lines in any textbook? It may be in an obvious place, I haven't really looked. :-) --Steve (talk) 20:32, 20 January 2012 (UTC)

Done. Kittel pages 194-196 is the same explanation. :-D (Thanks Nanite for pointing that out.) --Steve (talk) 16:12, 7 June 2013 (UTC)

Very Good Example, simply the Best for intuitive understanding, and that it's for Hole in semiconductors (problematic and uncleared thing)!! Nice Work!! --Vanquisher (talk) 18:54, 7 June 2013 (UTC)

In a normal metallic conductor, is current conducted only by electrons, or also by electron holes?

In high school I saw that the charges conducting electricity were really conducted by electrons, then later I saw semiconductors. I now have the impression that in metals both electrons and electron holes are responsible for conduction. Is this right? — Preceding unsigned comment added by 83.134.176.120 (talk) 06:23, 8 May 2012 (UTC)

From the point of view of elementary particles, metals and semiconductors are made of electrons and protons and neutrons. Out of these three, only electrons move to carry current. That's probably what your high-school teacher meant.

BUT the electrons in semiconductors and metals move in counterintuitive and complicated ways, because they are interacting with each other and with the protons; it's very different from how we usually think of particles moving. So people invented the notion of quasiparticles: Imaginary particles with different properties than electrons, that would give rise to the actual currents you get from the weird electron motion. Semiconductors can be explained very accurately by having two types of quasiparticles: An electron quasiparticle (like an electron but with the wrong mass) and a hole quasiparticle (like an electron but with the wrong mass and the opposite charge). I believe that metals usually have only one kind of quasiparticle and it has similar properties to an actual electron. But not always! Some metals have the "wrong" sign of Seebeck coefficient or Hall effect, an indication that they have positively-charged quasiparticles. --Steve (talk) 12:46, 8 May 2012 (UTC)

Some metals have very complicated band structure, including both electron and hole bands. Aluminum, the metal most used for long-distance power transmission, has almost equal electron and hole bands. In higher magnetic fields, the bands shift, and the hall coefficient goes positive. It might be that alkali metals only have an electron band, but as you add outer shell electrons, the band structure gets more complicated. Gah4 (talk) 17:09, 4 May 2015 (UTC)

Discrepancy Betweeen Electron Hole Article and Dirac Equation Article

From http://en.wikipedia.org/wiki/Electron_hole "The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice. It is different from the positron, which is an actual particle of antimatter, whereas the hole is just a fiction, used for modeling convenience."

From http://en.wikipedia.org/wiki/Dirac_equation#Hole_theory "In certain applications of condensed matter physics, however, the underlying concepts of "hole theory" are valid. The sea of conduction electrons in an electrical conductor, called a Fermi sea, contains electrons with energies up to the chemical potential of the system. An unfilled state in the Fermi sea behaves like a positively-charged electron, though it is referred to as a "hole" rather than a "positron". The negative charge of the Fermi sea is balanced by the positively-charged ionic lattice of the material."

I am not an expert on the subject but I would like to see this resolved! — Preceding unsigned comment added by Dudekahedron (talk • contribs) 15:04, 12 August 2012 (UTC)

I do not think these paragraphs contradict each other ... if you do think that, could you explain a bit? --Steve (talk) 22:39, 12 August 2012 (UTC)

It takes more quantum mechanics that I know how to explain to show the difference, but if you do it right, I believe that holes are no more fictional than positrons. Both come out of solutions to differential equations used in quantum mechanics, one from solid state physics, the other from high-energy physics. Gah4 (talk) 17:13, 4 May 2015 (UTC)

Electron-hole pairs

I found this page looking for an article (or link) on electron-hole pairs. Should there be such a page? Or did I miss it? Gah4 (talk) 17:15, 4 May 2015 (UTC)

The link electron-hole pair redirects to the page carrier generation and recombination. If you want to write a better description of electron-hole pairs, I would suggest adding it to that article, rather than creating a new one. Of course if the pair is bound together then that's in the scope of the exciton article... --Steve (talk) 17:50, 5 May 2015 (UTC)

Most likely that is just fine. Somehow I found this page instead. Though carrier generation and recombination is written in terms of semiconductor device physics. I was looking for one to link from Photography related to the physics of silver bromide. Light also creates e-h pairs in AgBr, which is the basis for AgBr photography, but isn't exactly the same as in device physics. Gah4 (talk) 18:20, 5 May 2015 (UTC)

Hole superconductivity

There is a new section on "hole superconductivity" that sounds suspiciously like original research. I didn't yet decide to remove it, but I do wonder. The part about the band structure of superconducting metals should be easy to find a reference for, and that is probably fine. But it looks like it goes farther, including disagreeing with BCS. Gah4 (talk) 05:05, 23 September 2015 (UTC)

I just deleted it. Even if the theory is notable and referenced to reliable sources, I think it's undue emphasis. Holes are such a fundamental concept that they play a role in literally every aspect of the electronic behavior of solids. Of course holes are important in superconductors, just as they are important in magnetism, in the quantum hall effect, in the thermoelectric effect, in lasers, in transistors, etc. etc. --Steve (talk) 00:53, 28 October 2015 (UTC)

Confirm "detailed picture" ?

The [Picture] section states:

Electrons near the top of the valence band behave as if they have negative mass

However the [Mass] article states:

For energy eigenstates of the Schrödinger equation, the wavefunction is wavelike wherever the particle's energy is greater than the local potential, and exponential-like (evanescent) wherever it is less. Naively, this would imply kinetic energy is negative in evanescent regions (to cancel the local potential) ... this means that any evanescent portions of the wavefunction would be associated with a local negative mass–energy

And the [Mass] article states:

One remarkable property is that the effective mass can become negative, when the band curves downwards away from a maximum

Together, this suggests the section should read:

Electrons near the bottom of the valence band behave as if they have negative mass

— Preceding unsigned comment added by 100.8.0.181 (talk) 20:26, 25 October 2016 (UTC)

I believe they are two different effects, though I am not sure I can explain why. Electrons in a full band aren't effected by an electric field, unless it can supply enough energy to get them out of the band. Electrons at the top of a band have negative effective mass, though at the bottom have to have positive effective mass. Gah4 (talk) 23:31, 25 October 2016 (UTC)

The section you quoted from "Negative mass" is weird and confusing. I think you should ignore it—in fact it probably should be deleted. If an electron wavefunction has an evanescent tail—an extremely common situation—it does not mean that the electron has "local negative mass-energy" in any sense I can understand. I think the author of that section was basically confusing and conflating some largely-unrelated concepts. --Steve (talk) 19:50, 27 October 2016 (UTC)

You need the negative (effective) mass to explain the difference between the moving empty seat analogy, and actual holes. But evanescence is related to negative kinetic energy and tunneling, where the mass is positive. I suspect that the article could explain the difference between effective mass and real mass better. Gah4 (talk) 20:40, 27 October 2016 (UTC)

A bit of history

It would be nice if someone would add a bit of history about who actually introduced the concept of holes into condensed matter and how it is related to the concept of holes introduced by Dirac for elementary particles (Fermions). — Preceding unsigned comment added by Iskander32 (talk • contribs) 22:46, 12 February 2019 (UTC)

Yes, it would be nice to know the story better. As well as I know it, during WW2, point contact silicon rectifiers were used in radar. At one point, someone had a silicon rod that was (they didn't have the name yet) p-type on one end, and n-type on the other. That is, when you made a point contact rectifier, it had one polarity one one end, and the opposite on the other end. This then led to intentional doping of semiconductors p-type and n-type, and PN junctions. The transition from point contact transistors to alloy junction transistors, and then better understanding of bipolar transistor theory would have led to the idea of holes. As is usual with inventions, much of the understanding that should have come first, actually came later. Gah4 (talk) 21:20, 14 February 2019 (UTC)

missing just a few electrons

The number of holes might be small compared to the number of atoms, and still be large. Each band has two states (which may or may not contain electrons) for each atom in the crystal, so about 10²³ for a small sample. One ampere is about 10¹⁹ electrons (or holes) per second, so we are not talking about a few electrons in most cases. Gah4 (talk) 15:28, 13 March 2019 (UTC)

I agree that a reader could potentially be confused when we use "just a few" to describe maybe a quintillion missing electrons per cm³. You're welcome to tweak the wording, e.g. "missing just a few (relative to the total number)" or "missing just a small fraction of its electrons" or whatever. --Steve (talk) 13:42, 15 March 2019 (UTC)

I am not so sure what happens when it gets to be much more. It gets more interesting in metals, where bands are closer to half full. As well as I know it, a group II metal, which has the number of electrons to fill a band, instead has one that is a little less than half, and another a little more than half. Less than half will be an electron band, and more than half a hole band. But even for semiconductors, there can be many holes in an almost full band. Gah4 (talk) 14:10, 15 March 2019 (UTC)

particles

There seems to be much discussion about hole being, or not being, particles. In solid-state physics, hole and electrons are both treated as waves, and not particles. The confusing thing, for many of us, is that even though they are waves, they still come in discrete amounts. You can have one or two, but not 1.5 of them. On the other hand, electrons can travel through vacuum, as in vacuum tubes, while holes can't. But that doesn't happen in solid-state physics. It doesn't seem to me, though, that the idea of quasiparticle makes this any more obvious to someone who doesn't understand Bloch waves. It also helps to understand Fermi exclusion, which is the thing that allows for holes in the Fermi sea. In any case, I vote for less discussion of quasiparticles. Gah4 (talk) 01:12, 30 June 2021 (UTC)