In an n-type semiconductor with donor concentrationN D and acceptor concentratio

Question

In an n-type semiconductor with donor concentrationND and acceptor concentration NA , whereND>NA a. State and explain the charge neutralityequation b. State the mass action law and explain what itrepresents c. Solve the above stated two equations to findn and p , (find them as expressions functions ofni , ND and NAonly no numbers) In an n-type semiconductor with donor concentrationND and acceptor concentration NA , whereND>NA a. State and explain the charge neutralityequation b. State the mass action law and explain what itrepresents c. Solve the above stated two equations to findn and p , (find them as expressions functions ofni , ND and NAonly no numbers)

Explanation / Answer

a) In a n-type semiconductor, ND represents thedonor atoms i.e. number of atoms which have given away their extraelectrons and have acquired ‘+ve’ charge. When anelectron leaves an atom it creates a ‘+ve’ charge thereso the charges are balanced with respect to the donor atoms. Donoratoms represent the fixed ‘+ve’ charges.

Similarly for acceptor atoms (NA) the charge isbalanced.

Let the total concentration of electrons, n0 = n +(ND no of electrons from donor atoms)

The total concentration of holes, p0 = p +(NA no of holes from acceptor atoms)

n and p are intrinsic concentrations, so they are equal.

Now writing the mobile and fixed charges of one polarity on 1side and of opposite polarity on other side we get

n0 + NA = p0 +ND

This is the charge neutrality equation.

b) The mass action law states that the product of concentrationof electron and hole of a doped semiconductor is equal to thesquare of intrinsic concentration of carriers of undopedsemiconductor at a particular temperature.

n . p = ni2

It represents that temperature remaining constant the productfor concentrations of electron and holes (for any value of dopingconcentration) is always equal to ni2 at thattemperature.

c) For an n-type semiconductor, the concentration of donor atomsis higher than acceptor atoms. ND >>NA

So, n0 =ND                      (nearly equal)

From mass action law

n0 . p0 = ni2

p0 = ni2/ND

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