- #1

- 25

- 0

## Homework Statement

This isn't actually a homework question, but in my semiconductors textbook, the following equation has been given:

[tex]E_f = E_g - k_BTln(\frac{n_0}{N_d - N_a})[/tex]

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

## Homework Equations

[tex]N_d - N_a[/tex] (Where Nd = donor level and Na = acceptor level)

Also: [tex]E_F = E_g - E_d[/tex]

## The Attempt at a Solution

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

[tex]n = n_0e^{\beta(E_f - E_g)} = n_0e^{-\beta E_d}[/tex]

where beta = 1/kT

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