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

## Homework Statement

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.

## Homework Equations

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

## 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?