how to calculate working function

[mldavidhuang]

Can ATK calculate working function of a certain material?

[zh]

Of course, you can. Please check here:
http://quantumwise.com/forum/index.php?topic=141.0

[mldavidhuang]

Thank you!

[mldavidhuang]

The script can help me calculate the working function of metal, what if the case of other material like graphene nanoribbon or bulk MoS2?

[zh]

Basically, they can also be used for the systems mentioned by you. In these cases, the Fermi level is taken as the valence band maximum.

[Anders Blom]

We have published a new tutorial on computing the work function with ATK 11.2 today.

[ramkrishna]

Does the approach to calculate work function for Hydrogen passivated  [100] SiNW (built by  nanowire custom builder) will be same like that tutorial? If so, then how can I specify the ghost atom (or atoms)?

[Anders Blom]

Sure, the basic idea is the same, but since your system is now periodic in Z, the relevant boundary condition (Dirichlet) should be applied on the X/Y boundaries. You can try without ghost atoms first, they are not absolutely necessary, it's just a way to get the electron density to not end so abruptly on the surface.

Or, as an alternative, you can always extend the range of the basis set; export the script using "Show defaults" in the Script Generator to see how the basis set radius is defined.

If you want to use ghost atoms, place a couple of them close to the surface, around the wire. There's no rule where they must be (except they must be within coupling range of the other atoms, of course), it's just a way to place some density in the vacuum.

[ramkrishna]

I have calculated the  work function of bulk Silicon and it gives 4.9 eV which is quite near the theoretical value (4.6 - 4.85 eV) but  for Hydrogen passivated  [100] SiNW (built by  nanowire custom builder) the work function value is very much lower than the bulk value (3.97 eV) for radius 10A. But generally for SiNW the value of work function should show roughly an exponential decay with increasing size and  converges with the bulk value for higher radius (Ref. http://www.springerlink.com/content/r92156705275l566/ ). I can't understand whether my calculation is correct or not for [100] Silicon nanowire. Attached please find the file for my DFT calculation. Please help me.

[Anders Blom]

I see a few differences compared to the article you refer to, they apparently have a cylindrical wire, while yours is more squarish.

Also very importantly your boundary conditions are not correct. The reason we use Neumann and Dirichlet in the slab case is that you only have vacuum on one side, or at least that's what you are trying to simulate - the surface is supposed to be infinitely deep. In the nanowire case you have vacuum all around, so provided you have a sufficiently large vacuum padding (which needs to be checked carefully) it would be ok to set Dirichlet conditions on both sides in X and Y.

Alternatively you can leave them periodic, and compute the effective potential at the boundaries, and subtract this from the Fermi level.

Whether or not you will need ghost atoms will be interesting to see; the comparison with the plane-wave calculation will be helpful in determining this. However, again, note that you need to make sure the shape of the wire matches the article, or else it's hard to compare anything.

[ramkrishna]

Dear Sir,
      Actually I just wanted to say about the trend of work function only from that reference. My system is a square wire, not cylindrical.

For the boundary conditions, I have checked already with Dirichlet conditions on both sides in X and Y but it gives same result. I have also tried with ghost atoms but can''t see any change. So, if I want to stick with this procedure then what should I do?

If I will try to  compute  the effective potential at the boundaries, then what is the procedure to calculate that ?

Regards
Ramkrishna

[Anders Blom]

I understand

Another major difference is that your wire is (100), the publication deals with (110).

Beyond this, your approach seems ok, provided it's carried out correctly, but to analyze the results and draw the proper conclusions you have to investigate it carefully an motivate the results, e.g. by comparing the changes in surface density compared to the bulk 100 surface, which is closely related to reduction or increase of the work function, etc etc. This is why research is fun!

[Anders Blom]

The approach to compute the effective potential on the edges is not recommended. It's how other codes do it, which don't have the option to specify other than periodic boundary conditions. That's why I mentioned it, to indicate that you can do it differently (better, I would say) in ATK. As long as you have enough vacuum and Dirichlet conditions, you should be fine.

[sitangshu]

Hi,

Can you let me know whether the work function (W) of a nanowire material is greater than or lower than its bulk value? If I increase the diameter of an intrinsic  SiNW, it is known that the Fermi level (Ef, as measured from the bottom of the conduction band minimum) decreases. Since W = Q - Ef, where Q is the vacuum energy level, a decrease in Ef results an increase in W. Thus, as I understand, increasing diameter of the intrinsic NW increases W. Is this approach ok? and is this formalism been taken in ATK?

Please reply.

Thank you.
******************
Sitangshu

[kstokbro]

I think it is very difficult to give a general rule about the work function for nanowires. It will depend on the change in bandstructure and the filling of the bands,
as well as the surface dipole of the nanostructure. Both effects will depend on the particular nanowire you are investigating.

I recommend that you follow the steps in the minitutorial: http://www.quantumwise.com/publications/tutorials/mini-tutorials/134
and calculate the workfunction of the systems,