Charge carriers per atom in graphene

In summary, the conversation discusses the individual contributions of carbon atoms to the charge carriers in graphene. The speaker has a plan to find this information by calculating the number of atoms per unit area and dividing the carrier density by this number. They have also derived the formula for the total number of atoms and cells at each level and have determined the limit to be 2 atoms per cell. The other speaker confirms that this calculation is correct and wishes the speaker luck with their research on graphene's atomic structure and its effect on charge carriers.
  • #1
kishtik
100
0
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.
 
Physics news on Phys.org
  • #2
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!
 

1. How many charge carriers are there in a single atom of graphene?

The number of charge carriers in a single atom of graphene is difficult to determine as it depends on several factors, such as the type of doping and the level of electron mobility. However, it is estimated that a single atom of graphene can have around 4-6 charge carriers.

2. Can the number of charge carriers per atom in graphene be controlled?

Yes, the number of charge carriers in a graphene atom can be controlled through a process called doping. This involves adding impurities or foreign atoms to the graphene lattice, which can either increase or decrease the number of charge carriers.

3. How does the number of charge carriers affect the conductivity of graphene?

The number of charge carriers in graphene directly affects its conductivity. More charge carriers mean more available paths for current to flow, resulting in higher conductivity. This is why doped graphene, with a higher number of charge carriers, has higher conductivity than pure graphene.

4. Are there any limitations to the number of charge carriers in graphene?

Yes, there are limitations to the number of charge carriers in graphene. As the number of charge carriers increases, the mobility of electrons decreases due to increased scattering. This can lead to reduced conductivity and other negative effects on the material's properties.

5. How does the number of charge carriers in graphene affect its potential applications?

The number of charge carriers in graphene is crucial for its potential applications. For example, in electronics, a high number of charge carriers is desirable for high-speed devices, while a low number of charge carriers may be needed for applications in optoelectronics. Understanding and controlling the number of charge carriers in graphene allows for fine-tuning its properties for specific applications.

Similar threads

  • Advanced Physics Homework Help
Replies
1
Views
895
  • Advanced Physics Homework Help
Replies
7
Views
6K
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
2
Views
2K
  • Advanced Physics Homework Help
Replies
2
Views
819
  • Advanced Physics Homework Help
Replies
1
Views
7K
Replies
7
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
916
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
Back
Top