# Carbon nanotube transmission

Hi friends,

I've calculated the transmission spectrum of ideal carbon nanotubes for various applied voltages on them. I obtained the transmission spectra shown below for various bias voltages. However, I could not interpret why the transmission spectra changes so much with the bias voltage.

I have to explain the variation in the transmission spectrum analytically. For the best, I need the transmission spectrum function which will have some physical parameters that can be related to the applied voltage. Could anybody please help? Any help will be appreciated.

http://img268.imageshack.us/img268/4789/87209245.png [Broken]

Regards,
carbon9

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## Answers and Replies

How did you calculate the transmission spectrum in the first place?
What chirality of carbon nanotube is the simulation for, as only 1/3 of nanotubes are metals and 2/3 are semi-conductors.
Did you use DFT or Tight binding, or some other theory.
I don't think you supplied nearly enough information.

What theory are you using here?

It's a metallic CNT because at 0 eV, the transmission is 2, which means there are at least 2 conducting modes even at no bias. (no bandgap)

But I have no idea what you mean by "different biases" because to read this plot, you need to interpret the x-axis (the difference between the two contacts' electrochemical potential) as the BIAS.

So what other "bias" do you mean here? Is there a third terminal? Do you mean to say there exists a "gate" voltage also?

Another thing that's probably wrong: Why would I ever see a DECREASE in conductance
for increasing voltage?

Unless you are considering a complicated structure (something like a double-barrier etc..) it's nonsensical to see a decrease in conductance...

Post some more information and let's see

Thanks for your interest.

* I used (6,6) CNT (metallic).
* I used the software: ATK.2008 from Atomistix (Quantumwise).
* There is no third electrode. The CNT is connected to bias voltage from its right and left ends.
* x-axis is the energy of the electron whose transmission probability is given in the y-axis if it is injected by the supply voltage.
* I applied 0V, 1V and 2V bias voltages between the ends of the CNT and then obtained the transmission spectra as shown in the figure.
* I think, the important point is that the transmission spectrum shows a decreasing trend as the voltage applied between the two ends of the CNT is increased.
* I'm trying to obtain an analytical formulation of the transmission spectrum function using the standard Landauer-Büttkiker Approach.

Regards,

What kind of scattering is assumed here?
as I said there are several issues, fluctuating transmission doesn't make snse.

and WHY would the transmission spectrum show a decreasing trend? Do you have a simple reason for that or is it just something that comes out of your code?

Try NEGF-Landauer it'll be much cleaner.

Thanks.

It looks kinda fishy that the conductances are not exact integers for vanishing bias. For a perfect nanotube, the conductance should simply equal the number of propagating modes. And as said before, it does not really make sense that the transmission/conductance fluctuates like that. And as for the finite bias results, does the software calculate the conductance using the linear response result
$$G=G_Q \int_{E_F-eV/2}^{E_F+eV/2} dE T(E)$$?
This is not a good idea for as strong bias voltages as 1 eV, for which non-equilibrium methods should be used (and even they might not be that realistic).

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