Concentration of electrons in the conduction band in n type semi conductor

In an n-type semiconductor, the concentration of holes in the valence band is low, while the concentration of free electrons in the conduction band is high. This is because the n-type semiconductor has been doped with impurities that introduce additional free electrons into the crystal lattice.

Let Ed be the concentration of donor level and Nd be the concentration of donor atoms. Then concentration of ionized donor (Na+) = [1- f (ε)]Na. Here f(ε) = F-D distribution for electron.

If Ec be energy of valance band edge and me the effective mass of electron. Then concentration of electrons in the conduction band

Let p be the concentration of holes in the valance band. Then

At T = 0k, Ef lies between the top of the donor level and the bottom of the conduction band. As the temperature is increased, Ef drops and approaches towards the centre of forbidden gap at extremely high temperature thereby rendering n type semiconductor on intrinsic semiconductor.

Substituting equation 3 in equation 2

is donor ionization energy.

Equation 4 gives the concentration of electron in the conduction band of n type semiconductor.

The concentration of free electrons in the conduction band of an n-type semiconductor can be controlled by adjusting the amount of doping impurities added to the semiconductor. The higher the concentration of impurities, the higher the concentration of free electrons in the conduction band, and the better the semiconductor will be for certain electronic applications.

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