Graphene Device Length

[Emda]

I have a 40 Angstorm long bulk 2D infinite graphene sampled in the C direction 5 times, how long is the effective length of the graphene device simulated?


In another words, how to know the exact length of your structure depending on the sampling points you take?

[kstokbro]

I guess with sampled you refer to the k-point sampling?
if you have n=5 it correspond to the gamma point calculation of a 5 times longer device.

(This only hold for n an odd number, since even number n does not sample the gamma point)

[Anders Blom]

But, not to confuse anything here - the length of the system doesn't change because you change the k-point sampling. It's important you understand what the concept of k-point sampling really means first - there are many, many posts on this forum and the internet in general about this.

[Emda]

MY DEVICE:
CENTRAL (BULK 2D GRAPHENE) with length of 2.85 nm.
LEFT & RIGHT ELECTRODES OF THE SAME GRPAHENE AS WELL. 8 Angstorm each.

I need to simulate 100 nm device.

So I will sample it 35 (100nm/2.85nm) times in the C axis.

Does this do the job?

[Anders Blom]

No, that is precisely how it doesn't work. If you want to simulate a device of length X, you have to make it length X. However, a 100 nm device is not really ballistic, so simulating it on the level that ATK does might not be that relevant...

[Emda]

For the device shown on the picture on the attachment, this device is a 2d Graphene bulk infinite in the Y Direction, because there is no vaccum space. However, does ATK simulate it with long or short electrodes, as shown in the 2 figures attached with it. In other words, does the electrode length get repeated in the Y direction as well, or only the graphene?


They are png files,

If the electrodes length extends with the graphene in the Y direction, then I can assume that the electric field I inserted as Vg, is distributed uniformly across all the grpahene . Other wise it is only limited to the length of the electrodes, I inserted in the builder.

MY FINAL OBJECTIVE HERE, IS TO INSERT GATE VOLTAGE THAT WILL PRODUCE REALISTIC I-V VALUES, THAT WOULD BE CONFIRMED EXPERIMENTALLY.

[Anders Blom]

If you are looking for a system that is infinite in Y, you just need to use the smallest possible unitcell - and then k-points.

[Emda]

Indeed yes, my question is : if I use such "smallest possible unit cell", will the electrodes length extend infinity as well with the graphene (in the Y direction)?

Another question please, is this a ribbon , or graphene with graphene transmission curves and zero band gap K point?


What I am looking for is an infinite graphene (not ribbons) I-V curve.

[Anders Blom]

This is infinite graphene in the YZ plane.

[Emda]

How can it be infinite in the Z plane, when one of the constraints of the device configuration is having a finite central region? Can it be?

[Anders Blom]

Because the electrodes are repeated to infinity on either side, in Z. The central region is finite, yes, but each electrode is semi-infinite.

[Emda]

So the central region is infinite in the Y direction, yet it is finite in the Z direction.


Isn't this a ribbon structure? Isn't a ribbon periodic in 1 direction and finite in the other?

[Anders Blom]

The total structure is not finite in Z, it's still infinite. It's just that we treat a particular part (the central region) with a different numerical approach, in order to allow e.g. the application of a different chemical potential in the left and right electrodes - this would not be possible in a periodic structure in Z. More correctly put, we are sending in electrons from z=-infinity towards a finite scattering region, and then we extract the electrons towards z=+infinity.

A ribbon would be finite in Y but still infinite in Z.

[Emda]

Seriously thank you for your patience and help.

1- So if I extend the length of the central region of this device in the Z direction, the results (I-V) should be the same.Since, Unlike nanoribbonz, extending graphene structure does not affect its electrical transport properties....correct?


2- Do I need accurate transmission spectrum when calculating I-V or a jagged one would do the job as well? Avoiding Time consumption.

[Anders Blom]

1. That depends strongly on the gates. The gates modulate the electronic structure in the central region and the longer this part is, the larger the effective tunneling barrier might be, so the results can depend strongly on this. But it's not an effect of the length of the central region, more of the length of the gates (and potential, of course).

2. "Need" - for what? You are asking "can I get away with low accuracy results in order not to spend too much time on this" - well, if you want to publish the results, no. If you want to impress your professor, no. So, generally - no. Or, I mean, yes, you need accurate results if there should be any point to doing the simulations in the first place.