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What is Fermi level in semiconductor? Show that in intrinsic semiconductor Fermi level is always at the middle between the forbidden energy gaps.

Mumbai university > FE > SEM 1 > Applied Physics 1

Marks: 5M

Year: Dec 2013

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Fermi Level and Fermi energy

  • The energy of the highest occupied level at absolute zero temperature is called Fermi-energy.

  • The corresponding level is called Fermi level.

  • The energy levels are absolute zero above Fermi level are completely empty, while those below are completely filled

Let,

ne be the number of electrons in the semiconductor band.

nv be the number of holes in the valence band.

At any temperature, T>0K

ne=Nc.e(EcEF)/kT and

nv=Nv.e(EFEc)/kT

Where, Nc is the effective density of states in the conduction band.

Nv is the effective density of states in the valence band.

For best approximation, Nc=Nv

For an intrinsic semiconductor, nc=nv

Nc.e(EcEF)/kT=Nv.e(EFEc)/kT

e(EcEF)/kTe(EFEc)/kT=NvNc

e(Ec+EV+2EF)/kT=1   (Nc=Nv)

Taking ln on both sides,

(EC+EV2EF)kT=0

EC=EC+EV2

Thus, Fermi level in an intrinsic semiconductor lies at the centre of the forbidden gap.

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