# Homework Help: Effective density & Intrinsic carrier concentration

1. May 3, 2007

### Mimi

1. The problem statement, all variables and given/known data
Given "n=Nc*e-(Ec-Ef)/KT", prove "n=ni*e(Ef-Efi)/KT"

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

3. 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.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. May 4, 2007

### tnho

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

3. May 4, 2007

### 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.......

4. May 6, 2007

### tnho

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 dont know this makes the difference or not....

5. May 7, 2007

### Mimi

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