Determining Bandgap

[Arya]

Hi All,

I am new to ATK. I was trying to study effect of edge defects on bandstructure of graphene nanoribbon.
The way I proceed is to make an armchair GNR and repeat it for desired width along C direction. Then delete some edge atoms and setup bandstructure analysis.

Plotting the bandstructure I see a band near fermi level (attached image). I see gaps between the bands above as well as below the band near fermi level. This leaves me with the question where actually is the bandgap in this bandstructure (There are multiple places which seem devoid of any bands)? Any help is appreciated

Thanks,
-Arya

[Dipankar Saha]

It is quite obvious..., the kind of band diagram that you have got for a super cell having large no. of atoms..../ I guess, BG illustrates the property of any material....and, for that a unit cell of it (for example, which may be 4-AGNR, or may be a 6-ZGNR...etc. )should be sufficient.../ But, the issue is...when we have to find the effects of any scattering (due to any of the reasons.../say, Line edge roughness) on the electrical properties of a  nano ribbon or sheet... then Trans. Spectrum should be the right analysis to do, rather than the BG..... 

[Anders Blom]

This result can also be caused by not having edge termination (hydrogen atoms), so the band you see at the Fermi level could be a numerical artifact.

[Arya]

Thanks Dipankar Saha, I know transmission is the right thing to go for but I explicitly want to see at BG.

Thanks Anders, I will check again and let you know

[Dipankar Saha]

Arya
As you please...

[Dipankar Saha]

Dr. Anders Blom

Sir, in this context... I would like to ask you a few questions (for the sake of better clarity)...
1)What if I take a supercell (e.g., a sheet or, nano ribbon)...and Run the BandStruct Analysis???
/Actually, I did it with a sheet after incorporating defects..../ I have attached the diagram for the band struct.(in between GZ)...../
Now looking at the BG...
2) How can one say that, whether it will be anymore semiconducting or not? Will it behave like a metallic one??
(Where as, for the perfect Sheet...there was a large enough BG...referring towards the semiconducting nature of the material)

[Arya]

I too am looking for similar answer

[Nordland]

In simple terms: If you have band crossing the fermi level, then it is a metal, so one your graph I would say it is a metal.

[Dipankar Saha]

May be it sounds repetitive.... But still I must ask this....before reaching to any concluding point...../

So, as per you...any  sheet or nano-ribbon which was earlier showing semiconducting property...will all of a sudden start behaving like a metallic sample, by simply including a few defects (to bring the essence of real time scenario) here and there...!!!!

Then...the even more crucial point is...every time u have to make a channel of the device, using that material....you have to ensure that sheet/ribbon is absolutely perfect (Practically, which is hardly possible)....otherwise it will no more be showing S.C. property!!!!

Did you like to say these???

[Nordland]

I think there is many balls in the air, so let me try to answer them as best as I can one at the time in hand waving argumentation

1) It is important to remember that graphite is a semi-metal
2) When looking at atomic devices, the surface is very important. I have studied a lot of ZnO nanowire, and ZnO is a high-band gap semi-conductor.
    However in nanowires the surface of the nanowires gives rise to surfaces states and these surfaces results in that the nanowire becomes "metallic"
3) When a "small" defect is created, keep in mind that is a major perturbation of your system, and the effect of this may surprise you.
4) Your surface matter alot in a system that is two dimensional.

I think I will go write a paper about something

[Anders Blom]

In none of these posts has it been shown what kind of defect is introduced. If the defect manages to act as a donor or acceptor, then yes you could easily reach a situation where the dopant concentration is so high that you get a degenerate situation.

Or, if you are making edge defects and not terminating them properly with hydrogen, your band around the Fermi level is just a spurious numerical effect.

It's necessary to provide all relevant details of a particular result showing certain effects, before asking anyone to answer a generic question.

[Dipankar Saha]

Dr. Nordland....

Sir,
though all the four points those you have cited essentially correct, and very much helpful for understanding the issue...  Bt still the problem remains unsolved..... / Actually you are right, by saying that there are too many balls in the air...... May be  we have to consider all the different possible aspects....../

Anyways, thanks....

[Dipankar Saha]

Dr. Anders Blom

Sir,
defects introduced were line edge roughness.... So, may be ...it is possible... that the bands around the Fermi level are due to any spurious numerical effect....

Anyways, Thanks a lot....

[Nordland]

If I were to continue your work, this is the recipe I would follow:

• Calculate the bandstructure a ribbon that is semi-conductor
• Calculate the bandstructure for the same ribbon with your introduced defect
• Inspect the bandstructure of the two and determine what is the band gap in each. In the one case it will be a zero since it is metal, but it will give you something to determine if this semi-conducting ribbon is bordering to be a metal.
  
• In the semi-conducting ribbon I would first calculate HOMO Bloch-state and see where in space this orbital is located - is this a state localized at the surface or is the state evenly distrubted over the system or it is located to the 'core' of the ribbon.
• In the metalic ribbon, find the k-point which is closest to the fermi level and calculate the HOMO Bloch States in this point. Where it localized?

After you have do this analysis, I will understand much more. The most likely outcome of this analysis will be this is a surface state or defect state that has been introduced in the band gap - we don't know yet. If this is the case we would properly conclude that it is the high symmetry of the configuration of the ribbon that keep surfaces states from forming in the band gap, and almost any pertubation in this edge would make the system metallic.

If we have to derive anything from this - there is at least two possible outtakes from this, and it comes down to what we want to model and what we want to compare it against. If the perturbation caused on the edge causes bands to form in the band gap, it is likely that any perturbation or contamination would break the semi-conducting properties of this ribbon in an experiment and therefore it is unlikely that we will never be use this particular ribbon as semi-conductor. Alternative does the edge of a ribbon look different that we believe and the geometric model we have for a ribbon does not correspond to the reality - it might have a different termination of the edge, which is 'safer' in terms of being a semi-conductor.

[Arya]

Thanks Nordland for detailed insights !