Cross section area measurement

[perfetti]

Dear Everyone,
       I've a little problem here:
       I want to calculate the cross section area of a certain part in my device, however, it seems to be impossible in ATK. I want to know if there's any way to get the cross section area of any part, using the length scale of vnl.
       Attatched is a picture of the cross section. My problem is like if I want to get the cross section area of the CNT,what should I do.
       Thank you!
       Best regards.

[Anders Blom]

If we forget for the moment the technical aspect of actually extracting the number, how would you define the cross-section area in this case?

In many cases one cannot just use concepts designed and defined for one type of devices (3D bulk or planar device, for instance) and apply them to entirely different structure. I don't think a device of this type has a well-defined relevant cross section, but the main question is why would you need to define one in the first place? Most likely the quantity that is desired to compute by dividing with the area is also not relevant. For instance, the current/area (taking just an example) would be pretty useless here - the current itself is enough. The reason current/area is relevant in a larger device is that the entire device is very large (on the atomic scale) and the larger you make it the larger the current, but you want some normalized number. But for a nanotube like this you are looking at a single tube, so the relevant number when comparing is current/nanotube. The only time current/area would make sense (and again, I'm just assuming a particular quantity to normalize by area, it's not necessarily your case) is if your device is a bundle of nanotubes. And in that case, the relevant area is the cross section area occupied by each tube, so one should consider how densely you can pack the tubes.

Sorry for the long rant - perhaps I'm wrong about your particular case, but I think I'm write about many cases

[perfetti]

Ehh, thanks for your patience. Dr. Blom.

My professor wants to know the conductivity of each part(The Cu part, and the CNT part), to see the role of each in conductance.

I think the cross section area couldn't be as accurate, but I think there's a way to convert or estimate it.  Like the way to calculate the curvature of a distorted CNT.  You can equate the area as the area of a circle.

Anyway, it's just an assumption of mine.  I am not sure if there's a way to figure it out.
......

[Anders Blom]

So - this is indeed a perfect example of a case where the area should be not be used

In ballistic transport in general, and molecular electronics in particular perhaps, the conductivity is not a relevant quantity. The conductance is, however - but it's independent of the cross section! It's very important to understand the difference between these two concepts.

I also think it may be hard to separate the properties of the subsystems, provided they are coupled (and if they are not you could just as well simulate them separately). What you could do is compute the current density, and look at an XY cross section through the device and see how much current goes in each part. I don't know if it will work in this case, but it's worth a shot.

[perfetti]

Thanks Dr. Blom for your clarification.
Yes we don't have strong physics background.
I have three questions:
1)  When you're saying the conductivity is not a relevant quantity, do you mean that in the ballistic region, there's no such a quantity existing? Everything is only related to T?

2) Can you quantize the current density? In face I've calculated some, but it only shows vague contour and iso-surface which I can only use for qualitative analysis.

3) Not so relevant, but still unclear to me for a long time:
What's the difference between LDOS, transmission eigenstate, and current density?
Are they independent of each other or complementary?
I have calculated all of the three, but I think they have a similar pattern. So I may could save some time after selecting next time.

Thank you!

[Anders Blom]

1. The concept of conductivity is typically related to diffusive transport when scattering is involved. The importance of conductance is that it is independent of the length of the conductor, as is the case in ballistic transport, whereas conductivity is inversely proportional to the length (because the longer it is, the more scattering can happen). Conductivity is a material parameter, whereas conductance simply tells you "given this much voltage, how much current do I get" (at least in case the I-V relation is linear).

2. The current density is reported in Ampere / area. But I interpreted your question before as it was important to know much much of the current was going in the nanotube and how much in the copper, at least relative to each other, so then the current density should be able to show that.

3. They are related in a very clear sense. LDOS is a function of energy only and measures the available states and how they are distributed in space. The current density is, more or less, the LDOS integrated over energy, and the LDOS can be seen as the transmission eigenstates integrated over channels. For real proper statements of these relationships you have to go a bit deeper, but that gives you at least a reason why they are similar looking.