Question

I don't understand why both of these formulas describe a fermi level in an intrinsic semiconductor?

Ei = (Ev + Ec)/2 + 1/2 kT ln (Nv/Nc)

Ei-Ev = Eg/2 + 3/4kTln (mh*/me*)

One is Ei - Ev which is intrinsic fermi level minus valence band so how does that give the intrinsic fermi value?

Answer 1

In first equation fermi level is of intrinsic semiconductor lies in between forbidden energy gap.

But in equation 2, Fermi level of inttinsii semiconductor is taken with respect to bandgap energy and fermi level is given by half of the energy gap and if we assume top of the Valence band Ever as zero energy level then Ei will be Fermi level. Which is given as under,

both equation indicates fermi level but reference is different.

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