0
1.1kviews
Prove that the Fermi level lies exactly at the centre of the forbidden energy gap in case of an intrinsic semiconductor.
1 Answer
0
50views

It can be shown for intrinsic semiconductors that fermi energy level  lies midway between conduction band and valence band. The proof is as follows:

At any temperature (T>0K)

ne = number of electrons in conduction band

nv = number of electrons in valence band

We have, by definition of intrinsic semiconductors:

The number of electrons in conduction  band is given by

ne=Nce(ECEF)KT

The number of electrons in valence   band is given by

nv=Nve(EFEV)KT

Where,

Nc = effective density of states in conduction band

NV = effective density of states in valence band

For best approximation, we consider Nc = NV

For intrinsic semiconductors, nc = nv

Nce(ECEF)KT=Nve(EFEV)KT

NVNC=e(ECEF)KTe(EFEV)KT

NVNC=e(ECEFEF+EV)KT

NVNC=e(EC2EF+EV)KT

As NC = NV = 1;

we get,

e(EC2EF+EV)KT=1

Taking log on both sides, we get,

(EC2EF+EV)KT=0

EC+EV=2EF

EC+EV2=EF

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

Please log in to add an answer.