Editing Electron hole (section)

== Comparison to positron ==
A hole in semiconductor physics, defined as the absence of an electron in a nearly full valence band, has a formal analogy to the [[positron]] in [[Paul Dirac]]'s relativistic theory of the electron (See [[Dirac equation]]).<ref name=":1">{{Cite journal |last=Kohn |first=W. |date=1970 |title=Electrons, positrons and holes |url=https://linkinghub.elsevier.com/retrieve/pii/0025540870901054 |journal=Materials Research Bulletin |language=en |volume=5 |issue=8 |pages=641–654 |doi=10.1016/0025-5408(70)90105-4}}</ref> In both cases, the system is described as a filled sea of negative-energy or valence states, and the removal of an electron leads to a positively charged entity that can carry current. The analogy extends to their electromagnetic behavior: both holes and positrons have a charge that is equal and opposite to that of an electron. When an electron and positron collide, they [[Annihilation|annihilate]] each other and the energy is emitted as photons or other radiation. An analogous process, [[Carrier generation and recombination|recombination]], happens in semiconductors, and can be described as an electron falling to the empty hole state and filling it, emitting radiation.<ref name="d593">{{cite book |last=Simon |first=Steven H. |url=https://www.worldcat.org/title/853504907 |title=The Oxford Solid State Basics |date=2013-06-20 |publisher=OUP Oxford |isbn=978-0-19-968077-1 |publication-place=Oxford |page=183 |oclc=853504907 |access-date=2025-05-18}}</ref> 

However, there are also limitations to this analogy. Due to the symmetries of Dirac's theory, positron and electron have exactly the same mass, while holes and electrons in crystals generally have different masses.<ref>{{cite encyclopedia |title=Semiconductors, History of |encyclopedia=Encyclopedia of Condensed Matter Physics |publisher=Elsevier |last=Bassani |first=G. F. |date=2005 |editor-last=Bassani |editor-first=G. F. |publication-place=Amsterdam Boston |pages=325 |isbn=978-0-12-369401-0 |last2=La Rocca |first2=G. C.}}</ref> The positron is a real particle with positive [[inertial mass]] and rest energy, while the hole is a quasiparticle whose inertial mass is negative. For this reason the responses differ in non-inertial frames: in an accelerating crystal lattice, a positron lags behind, whereas a hole moves forward with the lattice. These differences also appear in composite systems; for example, [[Exciton|excitons]] (electron–hole pairs) move rigidly with the lattice and carry no net momentum, unlike [[positronium]] atoms (electron–positron pairs), which gain momentum and energy relative to an accelerating frame.<ref name=":1" />

The concept of an electron hole in solid-state physics predates the concept of a hole in Dirac equation, but there is no evidence that it would have influenced Dirac's thinking.<ref name=":0">{{Cite book |last=Pippard |first=Brian |title=Twentieth century physics |publisher=American Institute of Physics Press |year=1995 |isbn=978-0-7503-0310-1 |volume=III |pages=1296–1298 |chapter=Electrons in solids}}</ref>