Talk:Electron hole

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)

Spin of electron holes

"Conclusion: Hole is a positive-charge, positive-mass quasiparticle."

I have found this article very helpful and detailed. However, I noticed that it does not mention anything about the spin of electron holes. I have recently been trying to understand the idea that electron holes can (effectively) have spin just like electrons themselves. Would anyone with more knowledge on this be able to comment on what kind of statement could be added to this article regarding the spin of electron holes? Are there certain caveats or parameters that affect the spin? QB2k (talk) 22:46, 17 May 2025 (UTC)

The book Nazarov, Julij V.; Danon, Jeroen (2013). Advanced quantum mechanics: a practical guide. Cambridge: Cambridge University Press. pp. 99–100. ISBN 978-0-511-98042-8. defines a hole excitation of spin s and momentum hbar k as the removal of an electron with the opposite spin and momentum -hbar k. With this definition, the creation of a particle adds spin s and momentum hbar k to the system, regardless of whether it is an electron or a hole. (As a sidenote, the conditions considered currently in this article are unnecessarily restrictive, as the concept also applies in metals, not only in semiconductors with a full valence band. However, it is fine to consider hole in semiconductors separately, as the effective mass approximation is only applicable to them, but we need to add some discussion on more general level.) Jähmefyysikko (talk) 06:02, 18 May 2025 (UTC)

Thank you very much for the informative reply! If you don't mind, perhaps I will go ahead and add a comment somewhere in this article (perhaps at the end of the section titled "Detailed picture: A hole is the absence of a negative-mass electron") that cites the book you mentioned by Nazarov and Danon, and which says that the spin of an electron hole would be 1/2 based on the excerpt you referenced. Does that sound good? QB2k (talk) 21:29, 19 May 2025 (UTC)

Sounds fine to me. Jähmefyysikko (talk) 02:12, 20 May 2025 (UTC)