Explain recombination coefficient of intrinsic semiconductor and obtain the relation `n_(i)^(2)=n_(e )n_(h)`.

Explanation

Giving the energy to the semiconductor the creation of electron hole pair due to the migration of the electron to the conduction band is not a very stable situation.
The electrons and holes colloid with each other as per the law of thermodynamics and the temperature. The electron one again occupy the hole.
The creation of the electron hole pair and recombination process takes place at the same time.
In thermal equilibrium position the rate electron hole pair formation and the recombination is equal.
Recombination rate `prop n_(e ) n_(h)`
where `n_(e )` and `n_(h)` are electron and hole number densities respectively.
`therefore` The recombination rate `=Rn_(e )n_(h)`
where R is known as the recombination coefficient.
For intrinsic conductor `n_(e )=n_(h)=n_(i)`
`therefore` Recombination rate `Rn_(i)^(2)`
In thermal equilibrium,
`Rn_(i)^(2)=Rn_(e )n_(h)`
`therefore n_(i)^(2)=n_(e )n_(h)`