# Talk:Electron hole

WikiProject Physics (Rated C-class, High-importance)
This article is within the scope of WikiProject Physics, a collaborative effort to improve the coverage of Physics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
C  This article has been rated as C-Class on the project's quality scale.
High  This article has been rated as High-importance on the project's importance scale.

## 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?

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)

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)

"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)

## 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.

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 (talkcontribs) 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)

## 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 (talkcontribs) 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)