Local outlier factor: Difference between revisions

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{{Other uses|Mass action (disambiguation){{!}}Mass action}}
Under [[thermal equilibrium]] the product of the [[free electron]] concentration <math>n</math> and the free hole concentration <math>p</math> is equal to a constant equal to the square of intrinsic carrier concentration <math>n_{i}</math>. The intrinsic carrier concentration is a function of temperature.


The equation for the mass action law for [[semiconductor]]s is:<ref name="JNTU">{{Cite book | last = S | first = Salivahanan | coauthors = N. Suresh Kumar | title = Electronic Devices & Circuits | publisher = Tata McGraw Hill Education Pvt Ltd | year = 2011 | location = India | pages = 1.14 | isbn = 0-07-070267-5}}</ref>


:<math>np = n_{i}^{2}</math>
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==Carrier Concentrations==
In semiconductors, free electrons and [[electron hole|holes]] are the [[charge carrier|carriers]] that provide [[electrical conduction|conduction]]. For cases where the number of carriers are much less than the number of band states, the carrier concentrations can be approximated by using [[Maxwell–Boltzmann statistics|Boltzmann statistics]], giving the results below.
 
===Electron Concentration===
The free electron concentration ''n'' can be approximated by
:<math>n=N_c\text{ exp}\left[-\frac{(E_c-E_F)}{kT}\right]</math>
where
* ''E''<sub>c</sub> is the energy of the [[band diagram|conduction band]]
* ''E''<sub>F</sub> is the energy of the [[Fermi level]]
* ''k'' is the [[Boltzmann constant]]
* ''T'' is the temperature in Kelvins
* ''N''<sub>c</sub> is the effective density of states at the conduction band edge given by <math>\textstyle N_c=2\left(\frac{2\pi m_e^*kT}{h^2}\right)^{3/2}</math>, with ''m*''<sub>e</sub> being the electron [[effective mass (solid-state physics)|effective mass]] and ''h'' being the [[planck constant]].
 
===Hole Concentration===
The free hole concentration ''p'' is given by a similar formula
:<math>p=N_v\text{ exp}\left[-\frac{(E_F-E_v)}{kT}\right]</math>
where
* ''E''<sub>F</sub> is the energy of the [[Fermi level]]
* ''E''<sub>v</sub> is the energy of the [[band diagram|valence band]]
* ''k'' is the [[Boltzmann constant]]
* ''T'' is the temperature in Kelvins
* ''N''<sub>v</sub> is the effective density of states at the valence band edge given by <math>\textstyle N_v=2\left(\frac{2\pi m_h^*kT}{h^2}\right)^{3/2}</math>, with ''m*''<sub>h</sub> being the hole [[effective mass (solid-state physics)|effective mass]] and ''h'' being the [[planck constant]].
 
===Mass Action Law===
Using the carrier concentration equations given above, the mass action law can then be stated as
:<math>np = N_cN_v\text{ exp}\left(-\frac{E_g}{kT}\right) = n_i^2</math>
where ''E''<sub>g</sub> is the bandgap energy given by ''E''<sub>g</sub> = ''E''<sub>c</sub> &minus; ''E''<sub>v</sub>
 
==See also==
*[[Law of mass action]]
 
==References==
<references/>
 
==External links==
*[http://www.tf.uni-kiel.de/matwis/amat/semi_en/kap_2/backbone/r2_2_2.html  Doping, Carrier Concentration, Mobility, and Conductivity]
*[http://www-inst.eecs.berkeley.edu/~ee143/sp06/lectures/Semiconductor_tutorial.pdf Semi-conductor tutorial]
 
{{DEFAULTSORT:Mass Action Law(Electronics)}}
[[Category:Electronic engineering]]
[[Category:Empirical laws]]
 
 
{{Electronics-stub}}

Latest revision as of 17:06, 30 October 2014


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