# Intrinsic carrier concentration where did I go wrong?

1. Nov 16, 2017

### Kara386

1. The problem statement, all variables and given/known data
I've looked up the intrinsic carrier concentration of silicon, and what I've got isn't close. The question says given there are $2\times 10^{22}$ electrons per cubic cm in silicon, and the bandgap is $1.1$eV, what is the free electron concentration at room temperature?

2. Relevant equations

3. The attempt at a solution
My first thought is that since
$n_i = \sqrt{N_cN_v} \exp\left(\frac{-E_g}{2kT}\right)$
Maybe as T tends to infinity all electrons are free electrons so that $\sqrt{N_cN_v}=n_i$, but then subbing that back in at room temp would mean $10^{12}$ free electrons per cubic cm, so too high, but then that would be assuming the densities of states are constant at different temperatures, and they're not.

For silicon I can get around this by just looking up $N_c$ and $N_v$, but I have to repeat the process for diamond and the values aren't available. I do get the right order of magnitude estimate for diamond's carrier concentration just by using the same $N_c$ and $N_v$ as for silicon, presumably that's because they're similar in terms of crystal structure.

However, my professor assures me that all I should need is the electron concentration and the bandgap. I'd appreciate any help, been stuck on this for a while! :)

Last edited: Nov 16, 2017
2. Nov 21, 2017

### DrDu

How is the situation at T=0?

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