Mass action law (electronics)

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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[edit]

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[edit]

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[edit]

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[edit]

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 = EcEv

See also[edit]

References[edit]

  1. ^ S, Salivahanan; N. Suresh Kumar (2011). Electronic Devices & Circuits. India: Tata McGraw Hill Education Pvt Ltd. p. 1.14. ISBN 0-07-070267-5. 

External links[edit]