﻿ Mass action law (electronics)
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# Mass action law (electronics)

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Under thermal equilibrium the product of the free electron concentration n and the free hole concentration p is equal to a constant 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:

n p = n i 2 ^}

## Contents

• 1 Carrier concentrations
• 11 Electron concentration
• 12 Hole concentration
• 13 Mass action law
• 3 References

## 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  exp [ − E c − E F k T ] }\left}

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 Kelvin
• Nc is the effective density of states at the conduction band edge given by N c = 2 2 π m e ∗ k T h 2 3 / 2 =2\left^kT}}}\right^} , with me 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  exp [ − E F − E v k T ] }\left}

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 N v = 2 2 π m h ∗ k T h 2 3 / 2 =2\left^kT}}}\right^} , with mh 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 be stated as

n p = N c N v  exp − E g k T = n i 2 N_}\left-}}\right=n_^}

where Eg is the bandgap energy given by Eg = Ec − Ev

• Law of mass action

## References

1. ^ S, Salivahanan; N Suresh Kumar 2011 Electronic Devices & Circuits India: Tata McGraw Hill Education Pvt Ltd p 114 ISBN 0-07-070267-5

• Doping, Carrier Concentration, Mobility, and Conductivity
• Semi-conductor tutorial

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29.10.2014

Mass action law (electronics)
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