Local outlier factor: Difference between revisions
Jump to navigation
Jump to search
en>Sonicyouth86 m period before ref |
en>Chire Also use this source for Simplified-LOF, and as reference that this is a common mistake when using LOF. |
||
| Line 1: | Line 1: | ||
{{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> | |||
==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> − ''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}} | |||
Revision as of 09:25, 3 July 2013
I'm Fernando (21) from Seltjarnarnes, Iceland.
I'm learning Norwegian literature at a local college and I'm just about to graduate.
I have a part time job in a the office.
my site; wellness [continue reading this..]
Under thermal equilibrium the product of the free electron concentration and the free hole concentration is equal to a constant equal to the square of intrinsic carrier concentration . The intrinsic carrier concentration is a function of temperature.
The equation for the mass action law for semiconductors is:[1]
Carrier Concentrations
In semiconductors, free electrons and holes are the carriers that provide 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 Boltzmann statistics, giving the results below.
Electron Concentration
The free electron concentration n can be approximated by
where
- Ec is the energy of the conduction band
- EF is the energy of the Fermi level
- k is the Boltzmann constant
- T is the temperature in Kelvins
- Nc is the effective density of states at the conduction band edge given by , with m*e being the electron effective mass and h being the planck constant.
Hole Concentration
The free hole concentration p is given by a similar formula
where
- EF is the energy of the Fermi level
- Ev is the energy of the valence band
- k is the Boltzmann constant
- T is the temperature in Kelvins
- Nv is the effective density of states at the valence band edge given by , with m*h being the hole 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
where Eg is the bandgap energy given by Eg = Ec − Ev
See also
References
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534