Effective density & Intrinsic carrier concentration

[Mimi]

Homework Statement

Given "n=Nc*e-(Ec-Ef)/KT", prove "n=ni*e(Ef-Efi)/KT"

Homework Equations

Quasi-Fermi Energies..? Ef is Fermi level (extrinsic) and Efi is Fermi level (intrinsic). Ec is Fermi level (conduction).

The Attempt at a Solution

Very honestly, I cannot figure out how to start...
I know the value of "Nc", but I don't know how to deal with "ni" to prove the relationship.

 

[tnho]

Is there given any relation between Nc and ni ?
Can you say more about Nc? What is the expression of Nc??

 

[Mimi]

Nc=2[(2pi*m*KT)/h^2]^(3/2). (m=m*, effective mass for n)
ni^2=NcNv*e^-(Ec-Ev)/KT.
These are the only values I know...

 

[tnho]

Nc=2[(2pi*m*KT)/h^2]^(3/2). (m=m*, effective mass for n)
ni^2=NcNv*e^-(Ec-Ev)/KT.
These are the only values I know...

You have Nc and Nv, i guess Nv is something related to the holes, right?
having Nv=2[(2pi*m*KT)/h^2]^(3/2). (m=m*, effective mass for p)
and p=Nv*e-(Ef-Ev)/KT.

Consider intrinsic semiconductor case (ie n=p=ni)
we denote the intrinsic Fermi level as Efi and
n=Nc*e-(Ec-Ef)/KT
gives
ni=Nc*e-(Ec-Efi)/kT

Then, it can be seen that
n=ni*e(Ef-Efi)/KT

Notes: This result can be applied to any non-degenerate semiconductor (ie not just intrinsic/undoped semiconductor)

Once little thing i want to confirm is that,
what i learn for Nc is as a form of 2[(m*KT)/2pi*h^2]^(3/2) but not 2[(2pi*m*KT)/h^2]^(3/2).
Are you using cgs unit system?? I don't know this makes the difference or not...

 

[Mimi]

oh..I see.
Thank you so much tnho!