# Fermi level of n-type semiconductor Nd>Na>0

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1. Oct 17, 2015

### girlinphysics

1. The problem statement, all variables and given/known data
This isn't actually a homework question, but in my semiconductors textbook, the following equation has been given:

$$E_f = E_g - k_BTln(\frac{n_0}{N_d - N_a})$$

This is for the limiting case Nd>Na>0. I got a little confused as to where that equation has come from.

2. Relevant equations
$$N_d - N_a$$ (Where Nd = donor level and Na = acceptor level)
Also: $$E_F = E_g - E_d$$

3. The attempt at a solution

I think this means the fermi level is at donor level so I can write:

$$n = n_0e^{\beta(E_f - E_g)} = n_0e^{-\beta E_d}$$

where beta = 1/kT

Is this how they got to that equation? Just by rearranging for Ef?

2. Oct 22, 2015

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Oct 23, 2015

### girlinphysics

Unfortunately I haven't solved this problem, but I will try re-working it in case I have made it confusing. Thanks for the advice!