Local outlier factor: Difference between revisions

Revision as of 10:25, 3 July 2013

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my site; wellness [continue reading this..] Under thermal equilibrium the product of the free electron concentration $n$ and the free hole concentration $p$ is equal to a constant equal to the square of intrinsic carrier concentration $n_{i}$ . The intrinsic carrier concentration is a function of temperature.

The equation for the mass action law for semiconductors is:^[1]

np=n_{i}^{2}

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

n=N_{c}{\text{ exp}}\left[-{\frac {(E_{c}-E_{F})}{kT}}\right]

where

E_c is the energy of the conduction band
E_F is the energy of the Fermi level
k is the Boltzmann constant
T is the temperature in Kelvins
N_c is the effective density of states at the conduction band edge given by $\textstyle N_{c}=2\left({\frac {2\pi m_{e}^{*}kT}{h^{2}}}\right)^{3/2}$ , 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

p=N_{v}{\text{ exp}}\left[-{\frac {(E_{F}-E_{v})}{kT}}\right]

where

E_F is the energy of the Fermi level
E_v is the energy of the valence band
k is the Boltzmann constant
T is the temperature in Kelvins
N_v is the effective density of states at the valence band edge given by $\textstyle N_{v}=2\left({\frac {2\pi m_{h}^{*}kT}{h^{2}}}\right)^{3/2}$ , 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

np=N_{c}N_{v}{\text{ exp}}\left(-{\frac {E_{g}}{kT}}\right)=n_{i}^{2}

where E_g is the bandgap energy given by E_g = E_c − E_v

References

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External links

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[JNTU-1] 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

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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>
+==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}}

Local outlier factor: Difference between revisions

Revision as of 10:25, 3 July 2013

Contents

Carrier Concentrations

Electron Concentration

Hole Concentration

Mass Action Law

See also

References

External links

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Local outlier factor: Difference between revisions

Revision as of 10:25, 3 July 2013

Carrier Concentrations

Electron Concentration

Hole Concentration

Mass Action Law

See also

References

External links

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