# Mass Action law

Mass-Action law:-

Under thermal equilibrium for any semi conductor the product of number of holes and the no. of electrons is constant( and is independent of the amount of donor and acceptor impurity doping)

$\large&space;np&space;=&space;n_{i}^{2}$

n- electron concentration (or) number of electrons

p- hole concentration (or) number of holes

ni is the intrinsic carrier concentration

If a pure semi conductor is doped with N-type impurities, the no. of electrons in the conduction band(CB) increases above a level and no. of holes decreases below a level in the valance band (VB).

Similarly the addition of P-type impurities to a pure semi conductor increases holes in the valance band(VB) above a level and decreases the no. of electrons in conduction band(CB) below a level .

Charge Densities in N-type Semi conductor:-

Under equilibrium in a pure-Semi conductor $np=n_{i}^2$

when an N-type impurity is added then in N-type Semi-conductor $n_{N}p_{N}=n_{i}^2$ , the suffix N represents type of Semi conductor.

Number of electrons in N-type semi conductor= Number of donor atoms added+ number of holes in N-type semi conductor.

i.e, $n_{N}=&space;N_{D}+p_{N}$

since number of holes are very less in N-type material $n_{N}=&space;N_{D}$ ($\because&space;p_{N}$ is negligible)

$p_{N}&space;=&space;\frac{n_{i}^{2}}{n_{N}}$

$p_{N}&space;=&space;\frac{n_{i}^{2}}{N_{D}}$

$n_{i}$ – intrinsic  carrier concentration.

$p_{N}$ – number of hole concentration in N-type material.

$n_{N}$– number of electrons in N-type Semi conductor/ number of donor atoms.

Charge Densities in P-type Semi conductor:-

Under equilibrium in a pure-Semi conductor $np=n_{i}^2$

when an P-type impurity is added then in P-type Semi-conductor $n_{P}p_{P}=n_{i}^2$ , the suffix P represents type of Semi conductor.

Number of holes in P-type semi conductor= Number of acceptor atoms added+ number of electrons in P-type semi conductor.

i.e, $p_{P}=&space;N_{A}+n_{P}$

since number of electrons are very less in P-type material $p_{P}=&space;N_{A}$ ($\because&space;n_{P}$ is negligible)

$n_{P}&space;=&space;\frac{n_{i}^{2}}{p_{P}}$

$n_{P}&space;=&space;\frac{n_{i}^{2}}{N_{A}}$

$n_{i}$ – intrinsic  carrier concentration.

$n_{P}$ – number of electron concentration in P-type material.

$p_{P}$– number of holes in P-type Semi conductor/ number of acceptor atoms.

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## Author: Lakshmi Prasanna Ponnala

Completed M.Tech in Digital Electronics and Communication Systems and currently working as a faculty.