Editing Plasmon (section)

===Role===
Plasmons play a huge role in the [[optical]] properties of [[metal]]s and semiconductors. Frequencies of [[light]] below the [[plasma frequency]] are [[Reflection (physics)|reflected]] by a material because the electrons in the material [[Electric field screening|screen]] the [[electric field]] of the light. Light of frequencies above the plasma frequency is transmitted by a material because the electrons in the material cannot respond fast enough to screen it. In most metals, the plasma frequency is in the [[ultraviolet]], making them shiny (reflective) in the visible range. Some metals, such as [[copper]]<ref>
{{cite journal
 |date=1963
 |title=Energy Band Structure of Copper
 |journal=[[Physical Review]]
 |volume=129 |issue= 1|pages=138–150
 |bibcode= 1963PhRv..129..138B
 |doi=10.1103/PhysRev.129.138
 |last1= Burdick
 |first1= Glenn
}}</ref> and [[gold]],<ref>{{cite journal|author=S. Zeng|display-authors=etal|title=A review on functionalized gold nanoparticles for biosensing applications |journal=Plasmonics |volume=6|date=2011|pages= 491–506|doi=10.1007/s11468-011-9228-1|issue=3|s2cid=34796473}}</ref> have electronic interband transitions in the visible range, whereby specific light energies (colors) are absorbed, yielding their distinct color. In [[semiconductor]]s, the [[valence band|valence electron]] plasmon frequency is usually in the deep ultraviolet, while their electronic interband transitions are in the visible range, whereby specific light energies (colors) are absorbed, yielding their distinct color<ref>
{{cite book
 |last=Kittel |first=C.
 |date=2005
 |title=[[Introduction to Solid State Physics]] |edition=8th
 |publisher=[[John Wiley & Sons]]
 |page=403, table&nbsp;2
}}</ref><ref>
{{cite book
 |last=Böer |first=K. W.
 |title=Survey of Semiconductor Physics
 |volume=1 |edition=2nd
 |publisher=[[John Wiley & Sons]]
 |page=525
 |date=2002
}}</ref> which is why they are reflective. It has been shown that the plasmon frequency may occur in the mid-infrared and near-infrared region when semiconductors are in the form of [[nanoparticle]]s with heavy doping.<ref>{{cite journal |author1=Xin Liu |author2=Mark T. Swihart |title=Heavily-doped colloidal semiconductor and metal oxide nanocrystals: an emerging new class of plasmonic nanomaterials|journal=Chem. Soc. Rev.|date=2014|volume=43|issue=11 |pages=3908–3920|doi=10.1039/c3cs60417a|pmid=24566528 |s2cid=18960914 }}</ref><ref>{{cite journal|author1=Xiaodong Pi, Christophe Delerue|title=Tight-binding calculations of the optical response of optimally P-doped Si nanocrystals: a model for localized surface plasmon resonance|journal=Physical Review Letters|date=2013|volume=111|issue=17|page=177402|doi=10.1103/PhysRevLett.111.177402|bibcode=2013PhRvL.111q7402P|pmid=24206519|url=https://hal.archives-ouvertes.fr/hal-00877649/file/plasmon_Si_PRL_13.pdf}}</ref>

The plasmon energy can often be estimated in the [[free electron model]] as

:[[radiant energy|<math>E_{\rm p} = </math>]][[reduced Planck constant|<math> \hbar </math>]][[Plasma frequency|<math>\sqrt{\frac{n e^{2}}{m\epsilon_0}} = </math>]][[reduced Planck constant|<math>\hbar</math>]][[plasmon frequency|<math>\omega_{\rm p},</math>]]

where <math>n</math> is the [[conduction electron]] density, <math>e</math> is the [[elementary charge]], <math>m</math> is the [[electron mass]], <math>\epsilon_0</math> the [[permittivity of free space]], <math>\hbar</math> the [[reduced Planck constant]] and <math>\omega_{\rm p}</math> the [[plasmon frequency]].