Editing Debye length (section)

== In semiconductors ==

The Debye length has become increasingly significant in the modeling of solid state devices as improvements in lithographic technologies have enabled smaller geometries.<ref>{{cite journal| doi = 10.1021/nl071792z| volume = 7| issue = 11| pages = 3405–3409| last = Stern| first = Eric|author2=Robin Wagner |author3=Fred J. Sigworth |author4=Ronald Breaker |author5=Tarek M. Fahmy |author6=Mark A. Reed | title = Importance of the Debye Screening Length on Nanowire Field Effect Transistor Sensors| journal = Nano Letters| date = 2007-11-01|bibcode = 2007NanoL...7.3405S | pmid=17914853 | pmc=2713684}}</ref><ref>{{cite journal|last=Guo|first=Lingjie|author2=Effendi Leobandung|author3=Stephen Y. Chou|year=199|title=A room-temperature silicon single-electron metal–oxide–semiconductor memory with nanoscale floating-gate and ultranarrow channel|journal=Applied Physics Letters|volume=70|issue=7|pages=850|bibcode=1997ApPhL..70..850G|doi=10.1063/1.118236}}<!--| access-date = 2010-10-25--></ref><ref>{{cite journal |last=Tiwari| first=Sandip| author2=Farhan Rana| author3=Kevin Chan|author4=Leathen Shi| author5=Hussein Hanafi|year=1996 |title=Single charge and confinement effects in nano-crystal memories| journal=Applied Physics Letters |volume=69 |issue=9|pages=1232|bibcode=1996ApPhL..69.1232T|doi=10.1063/1.117421}}<!--| access-date = 2010-10-25--></ref>

The Debye length of [[semiconductor]]s is given:
<math display="block"> L_\text{D} = \sqrt{\frac{\varepsilon k_\text{B} T}{q^2 N_\text{dop}}}</math>
where
* {{math|''ε''}} is the dielectric constant,
* {{math|''k''<sub>B</sub>}} is the Boltzmann constant,
* {{math|''T''}} is the absolute temperature in kelvins,
* {{math|''q''}} is the elementary charge, and
* {{math|''N''<sub>dop</sub>}} is the net density of dopants (either donors or acceptors).

When doping profiles exceed the Debye length, majority carriers no longer behave according to the distribution of the dopants.  Instead, a measure of the profile of the doping gradients provides an "effective" profile that better matches the profile of the majority carrier density.

In the context of solids, [[Thomas–Fermi screening length]] may be required instead of Debye length.