# Free electron density conduction band

1. Nov 12, 2017

### Kara386

1. The problem statement, all variables and given/known data
How many free electrons are there in the CB? Diamond has a bandgap of $5.5$eV.Assume the material is at room temperature and that there are $2 \times 10^{22}$ cm$^{-3}$ electrons in the material. What does this mean for their use in semiconductor devices?

2. Relevant equations

3. The attempt at a solution
Probably I should use something like this equation:
$n = N_c \exp\left(\frac{E_F - E_C}{kT}\right)$
Where $N_c = \frac{8\pi\sqrt{2}m^{*3/2}}{h^3}\sqrt{E-E_c}$ is the effective density of states, and then multiply by the number of electrons in the material cm$^{-3}$. But there's quantities in there I don't know and can't calculate, like the Fermi energy (although is that half the gap?), and the energy of the conduction band, and the effective mass. I feel like this should be a simple question, but I can't see how to do it. It's possible, although unlikely, that I just have to look these quantities up, but if there's any other way I'd rather not do that. Thanks for any help! :)

2. Nov 17, 2017

### PF_Help_Bot

Thanks for the thread! 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? The more details the better.