Charge carriers per atom in graphene

[kishtik]

Hello. I'm trying to find the individual contributions of carbon atoms to the charge carriers in graphene. In other words, I'm trying to answer "How many charge carriers does one carbon atom supply?"

Here is what I've done so far:

Taking the max. carrier density as 10^13 1/cm^2 and the carbon to carbon bond length as 1.42*10^-10 m. My plan was:

1. Find the number of atoms for each unit cell of the chickenwire, (for large areas)
2. Divide by the area of the unit cell to find the number of atoms in unit area,
3. Divide the carrier density to the number of atoms per unit area to find the contribution from each atom.

Now, steps 2 and 3 are trivial of course, and I did the following for 1.:

Starting with one cell (calling this "level 0"), and adding the cells connected to it ("level 1"), and going on like this, adding the cells around what we already have at each level, we're adding 6 + 12L atoms at each level (L denoting the level number). So st level L, the total number of atoms is:

Sum(n=0 to L) (6 + 12n) = 6L^2 + 12L + 6

Now, we're adding 6L cells at each level, so the total number of cells for level L should be:

6 + Sum(n=1 to L) (6n) = 3L^2 + 3L + 6

Now, the number of atoms per cell should be the limit of the ratio of these as L --->infinity. The limit is obviously 2, so can I take 2 as the number of atoms corresponding to each cell and go on with step 2 of my plan?

Thank you in avance.

 

[Almsco]

Yes, you can take 2 as the number of atoms corresponding to each cell and go on with step 2 of your plan. You appear to have done the correct calculations and derived the correct result. Graphene is a two-dimensional material and it's quite interesting to study how its atomic structure affects the charge carriers. Good luck with your research!