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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)
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?
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)
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)
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...
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
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?
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? Ghos two 23:51, 16 October 2007 (UTC)
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.
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||
|
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)
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?
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)
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)
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...
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
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?
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? Ghos two 23:51, 16 October 2007 (UTC)
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.
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)