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QuantumATK => General Questions and Answers => Topic started by: baizq on May 4, 2011, 16:38

Title: Calculation the transport properties of graphene
Post by: baizq on May 4, 2011, 16:38
Dear all,

is the anyone who has done calculation of the transport properties of bulk graphene using ATK? I have tried by using bulk graphene as electrode and bulk graphene(over 50 angstroms in the transport direction), but the properies look like nanoribbon, with quantized transmission spectrum. The IV curve is linear, which I think it is wrong. Is this because I use less kpoints or something wrong with setting?

help,help..............
Title: Re: Calculation the transport properties of graphene
Post by: zh on May 5, 2011, 13:05
The gap of bulk graphene is zero. The linear behavior in the I-V curve may be reasonable.
Title: Re: Calculation the transport properties of graphene
Post by: nori on May 6, 2011, 04:06
Quote
but the properies look like nanoribbon, with quantized transmission spectrum

I guess that your transmission spectrum is step-like but the values are not integer.
Is this right?
If so, your calculation is reasonable, graphene should have such a feature.

I think over 50 angstroms is too long and you can reduce the size along z direction to 7-10 angstroms.
(Maybe even the primitive cell size is OK, I'm not sure because I don't know the detailed algorithm though...)
Title: Re: Calculation the transport properties of graphene
Post by: baizq on May 11, 2011, 14:58
Quote from: nori on May  6, 2011, 04:06
Quote
but the properies look like nanoribbon, with quantized transmission spectrum

I guess that your transmission spectrum is step-like but the values are not integer.
Is this right?
If so, your calculation is reasonable, graphene should have such a feature.

I think over 50 angstroms is too long and you can reduce the size along z direction to 7-10 angstroms.
(Maybe even the primitive cell size is OK, I'm not sure because I don't know the detailed algorithm though...)

Hi nori,

Thanks for your reply...
Actually this question is posted by my labmate...Actually I even do not know what bulk graphene is.... Actually he has gone to Malaysia...Actually we can neglect this question...
Anyway...Thanks very much !!

baizq
Title: Re: Calculation the transport properties of graphene
Post by: Anders Blom on May 13, 2011, 14:52
Just in case someone ends up here after searching :)

Converging the transmission spectrum of an infinite 2D graphene sheet is actually far from trivial. Although it may be sufficient with 9 or 15 in-plane k-points for the self-consistent loop (make sure to hit the K point), even with 200 points for the transmission spectrum the curve is rather jagged. So, such a system requires some careful considerations and patience, to ensure convergence of the results.
Title: Re: Calculation the transport properties of graphene
Post by: yongjunwinwin on July 11, 2011, 12:14
I am a little confused about how to calculate the transmission spectrum of an infinite 2D graphene, what is the device model? In the origin calculation of transport properties the scattering region between two electrode is always finite. In fact I try to build the device model  from the bulk model shown in attachments but it doesn't work, so could you explain in more details about the model and the difference between the device model of graphene nanoribbon?
Title: Re: Calculation the transport properties of graphene
Post by: zh on July 11, 2011, 12:54
The bulk graphene can also be described a supercell with orthogonal shape. The hexagonal one may be not suitable to build the device configuration of infinite system. Please  try the use of  orthogonal cell of graphene to build the device configuration.
Title: Re: Calculation the transport properties of graphene
Post by: yongjunwinwin on July 11, 2011, 16:13
I construct the bulk graphene device from an orthogonal shape(seen in the attachment),is that right, I find the difference between bulk graphene device and graphene nanoribbon is that there is no vacuum space along Y axis, does it make any sense? Another question is that in the calculation of such model, is the center region treated as infinite or finite?
Title: Re: Calculation the transport properties of graphene
Post by: zh on July 12, 2011, 03:13
Quote from: yongjunwinwin on July 11, 2011, 16:13
I construct the bulk graphene device from an orthogonal shape(seen in the attachment),is that right, I find the difference between bulk graphene device and graphene nanoribbon is that there is no vacuum space along Y axis, does it make any sense? Another question is that in the calculation of such model, is the center region treated as infinite or finite?
It seems right. The configuration in your attachment makes sense.  Due to the periodic boundary along the y direction, the center region will be treated as infinite since no vacuum region along the y direction.
Title: Re: Calculation the transport properties of graphene
Post by: yongjunwinwin on July 17, 2011, 02:55
Another question is how to set the k-sampling point for such system. I know for nanoribbon the reasonable k-sampling point is 1,1,100 for x,y,z for 1-D system, but when it comes to graphene, as the it is infinite along y, so the k-sampling point should be 1,9,9 or 1,9,100, is that sufficient? And the k-point sampling in transmission spectrum (1,1 for nA and nB) should also change? and how to change?
Title: Re: Calculation the transport properties of graphene
Post by: zh on July 17, 2011, 04:54
The setup of k-grid along the y direction depends on the width of unit cell along the y direction.  Maybe the k-grid of 1x9x100 may be OK. The best way is to do the convergence of k-grid. Yes, the k-point sampling in the transmissions spectrum should be changed. You can refer to the example of Fe/MgO/Fe system the k-dependent transmission spectra.
Title: Re: Calculation the transport properties of graphene
Post by: Anders Blom on July 17, 2011, 10:11
As pointed out in some other post on the Forum, infinite graphene is a bit trickier than a nanoribbon. While 9 k-points might be enough for the self-consistent loop, it should be checked (keep in mind the special nature of the K symmetry point, so a sampling of 10 or 9 or 11 points makes a big difference!) esp. when making a supercell. And then, for the transmission, be prepared to try 100, 200 or 400 points, otherwise the curves will be very jagged.

Title: Re: Calculation the transport properties of graphene
Post by: mldavidhuang on July 17, 2011, 12:03
If a sampling of 9, 10, 11 will make a big difference, then according to which can we decide the right choice?
And I was a little confused with the k-point sampling in the basis set and the k-sampling in transmission spectrum, what is the difference between them, those two parameters have any relationship and why transmission spectrum don't need k in z axis, it seems we need more k-sampling for transmission spectrum and why? Just as mentioned by zh, in the example of Fe/MgO/Fe I found the k for calculatore is 6, 6,100 for x,y,z while in the transmission spectrum the k sampling is 30, 30 for kA and kB
Title: Re: Calculation the transport properties of graphene
Post by: Anders Blom on July 17, 2011, 21:59
There is a physical reason why 9 k-points are better than 10, and also why 12 are better than 13 etc, which of course has to do with the point-like Fermi "surface" in graphene.

Indeed, the two k-point samplings are quite independent. In both cases the k-points are used to approximate an integral over the Brillouin zone, however the integrand is different, and depends differently on k. In the first case (the self-consistent loop) it's an expansion of the charge density, which rarely has any strong peaks or resonances as function of k, but may have a somewhat complicated functional form, and thus for some materials you only need 3x3 and for other 9x9 points. For the transmission spectrum, you may note in the FeMgO case that (in the parallel case) the majority transmission is well described with perhaps 11x11 points, but for the minority we may need 400x400 points. This is because the minority transmission has the character of resonant tunneling, with very sharp peaks which are hard to sample accurately.

In both situations, understanding the basic physics of the problem at hand is always essential.
Title: Re: Calculation the transport properties of graphene
Post by: mldavidhuang on July 18, 2011, 04:47
Is that right that more k-point sampling in the self-consistent loop will be more time consuming,e.g. (9,9) will cost more time than (3,3) ?

And how to figure out what k-point sampling is better? Is it based on experience or is there any general rule that we can follow?

Title: Re: Calculation the transport properties of graphene
Post by: Nordland on July 18, 2011, 09:57
9x9 is always better or the same as 3x3 in terms of accuracy and convergence - from case to case it might be enough with 3x3, and hence 9x9 will be a waste of time.
Title: Re: Calculation the transport properties of graphene
Post by: Anders Blom on July 18, 2011, 19:47
Of course more k-points take longer time.

For most system (esp. 3D bulk) you can always assume more k-points is more accurate, and a balance needs to be struck between computation time and accuracy, i.e. what is your acceptable level of inaccuracy for a lower k-point sampling than infinite.

Infinite graphene is a bit unusual when it comes to k-point sampling, however, which of course is due to the special Fermi "surface" at the K point.

Consider the following: below I list the top of the valence band and bottom of the conductance band at the K point for k-points up to (41x41).

Code
Nk	VB		CB
1	-2.83290807	-2.83266655
2	-0.09758413	-0.09734262
3	-0.00012076	0.00012076
4	0.00443931		0.00468083
5	0.02010983		0.02035134
6	-0.49142374	-0.49118223
7	-0.02140617	-0.02116465
8	-0.00251439	-0.00227288
9	-0.00012076	0.00012076
10	-1.78E-04		6.38E-05
11	-0.03717076	-0.03692925
12	-0.00330995	-0.00306843
13	-0.03310426	-0.03286275
14	-0.00071831	-0.0004768
15	-0.00012076	0.00012076
16	-2.31E-04		1.07E-05
17	-6.73E-05		1.74E-04
18	-0.000776		-0.00053449
19	-0.00167647	-0.00143496
20	-0.00037827	-0.00013676
21	-0.00012076	0.00012076
22	-2.00E-04		4.11E-05
23	-2.27E-04	1.48E-05
24	-0.00048527	-0.00024376
25	-0.00090307	-0.00066156
26	-2.62E-04		-2.07E-05
27	-0.00012076	0.00012076
28	-1.77E-04		6.41E-05
29	-2.40E-04		1.83E-06
30	-0.00035275	-0.00011124
31	-0.00058593	-0.00034442
32	-2.10E-04	3.17E-05
33	-0.00012076	0.00012076
34	-1.62E-04	7.91E-05
35	-2.26E-04	1.52E-05
36	-2.82E-04	-4.01E-05
37	-0.0004267	-0.00018519
38	-1.82E-04	5.95E-05
39	-0.00012076	0.00012076
40	-1.53E-04	8.89E-05
41	-2.10E-04	3.13E-05

This was computed with our Huckel model; since it's a symmetry-related result, the particular method has less of an influence on the conclusions, although in general the Huckel model is just as accurate (if not more, sometimes) for graphene, when using the Cerda basis set. The calculation of all results took 1 minute on my laptop, using the attached script, so there's no excuse for not doing a careful convergence study ;)

Now, if you look carefully, you will find that only for the following k-point samplings (Nk,Nk) will you have the two points straddling the Fermi level symmetrically:

Code
Nk = 3, 9, 15, 21, 27, 33, 39


So, quite simply: 3*an odd integer! Those are the ones you will want for infinite graphene in both 1D and 2D!
Title: Re: Calculation the transport properties of graphene
Post by: mldavidhuang on July 20, 2011, 18:50
Thank you for your detail explanation, but I have some questions:

what is the parameter you calculate in the code? and 41 is not belong to the group of 3*odd, so the example you list can be consider a exception ?

And the symmetry of the parameters of VB and CB means for what? is the symmetry of the parameter you list can be a test of the right choice of the k point without doing the convergence study?

Another question is for other 2D material, For example, BN or monolayer MoS2, for these system how to determine the right k-samping? Is the rule still work?
Title: Re: Calculation the transport properties of graphene
Post by: Anders Blom on July 21, 2011, 15:15
I'm afraid I don't quite understand your comments.

41x41x1 is just the largest k-point sampling I tried.

As mentioned in my previous post, VB and CB are the energies of the bottom of the conduction and top of the valence band at the K point.

The conclusions here are particular for graphene, but the method may be applied to other systems too.
Title: Re: Calculation the transport properties of graphene
Post by: mldavidhuang on July 22, 2011, 15:09
Sorry for making my comments unclear.
It seems you use the symmetry of energies of VB and CB as the standard to determine the validity of the k-sampling. So can we determine the validity of the k-sampling of other materials in the same way, I mean, also through the symmetry of the VB and CB at K point?
Title: Re: Calculation the transport properties of graphene
Post by: Anders Blom on July 22, 2011, 15:52
If the material is known to have a very special physics at the K point, like graphene has, then yes. Otherwise there is no reason to expect that.
Title: Re: Calculation the transport properties of graphene
Post by: yongjunwinwin on July 22, 2011, 16:13
If the material has not special physics at these points, just take bulk Si for example, how the test the valid of k-sampling?
Title: Re: Calculation the transport properties of graphene
Post by: Anders Blom on July 22, 2011, 16:17
Like you would converge anything: keep increasing the number of k-points until the quantity of interest doesn't change any more (within some acceptable accuracy, of course).
Title: Re: Calculation the transport properties of graphene
Post by: zh on July 23, 2011, 04:56
Quote from: yongjunwinwin on July 22, 2011, 16:13
If the material has not special physics at these points, just take bulk Si for example, how the test the valid of k-sampling?

Strongly recommend you to read this following paper:

Ann E Mattsson, Peter A Schultz, Michael P Desjarlais,
Thomas R Mattsson and Kevin Leung
Designing meaningful density functional theory calculations in materials science—a primer
Modelling Simul. Mater. Sci. Eng. 13 (2005) R1–R31
http://iopscience.iop.org/0965-0393/13/1/R01/
Title: Re: Calculation the transport properties of graphene
Post by: mldavidhuang on July 23, 2011, 12:28
Thanks for your reference !
Title: Re: Calculation the transport properties of graphene
Post by: esp on January 16, 2012, 11:21
I have create a simple GNR fet type device and have tried to follow the tutorial code .. i want to get the IV curve for a simple GNR ... code is below and attached image ..

It should be a 12,0 AGNR, gate voltage at 1V, electrodes at -0.1 and 0.1, .... IV curve is linear (only if I "symmetrize", otherwise it is a point) ... and i get flat conductance ... what am I doing wrong?

makeCfg() and doCalcs() are the only functions used for now ..
Title: Re: Calculation the transport properties of graphene
Post by: Anders Blom on January 16, 2012, 11:31
A few things to consider. First of all, you don't get an IV curve from a single calculation, you have to run it at different bias, otherwise indeed it's just a point on the curve, not a curve.

Second, take care with your dielectric and metallic regions; they are sticking out of the box, which means they get wrapped around, not a good idea. Keep everything inside the box, atoms and what.

Finally, don't expect too much from a perfect 1D conductor. The IV curve can be trivially obtained from a simple band structure analysis, but to run a real finite-bias calculation on a perfect system is not a good idea. The reason is, that since it's perfect there should be no resistance (in the ballistic regime we are considering in ATK). But if there is no resistance, there is no point for the bias voltage to drop across the structure - a finite bias and a finite current means there must be finite resistance.

It would be better to do something like the simple but non-trivial system in the VNL tutorial (http://quantumwise.com/documents/manuals/latest/VNLTutorial/index.html/chap.gnr.html), or the longer graphene tutorial (http://quantumwise.com/documents/tutorials/latest/BasicGrapheneTutorial/). Or, if you want gates included, the graphene device tutorial (http://quantumwise.com/documents/tutorials/latest/GrapheneDevice/).
Title: Re: Calculation the transport properties of graphene
Post by: esp on January 16, 2012, 18:34
thank you
Title: Re: Calculation the transport properties of graphene
Post by: esp on January 16, 2012, 20:53
I was unclear about the role of "the box" ... is there somewhere in the tutorials that explains this?
Title: Re: Calculation the transport properties of graphene
Post by: Nordland on January 16, 2012, 22:47
Quote from: Anders Blom on January 16, 2012, 11:31
Second, take care with your dielectric and metallic regions; they are sticking out of the box, which means they get wrapped around, not a good idea. Keep everything inside the box, atoms and what.

A small correction. Regions are not wrapped - this goes for both metallic and dielectric regions, but only the part inside the cell
is present in the calculation. Therefore your case the metallic region is disregard and you will not seen any effect of it.

As Anders explains one should be careful about deriving too much physics from a perfect metallic 1d systems, since the screening effect is almost infinite bad, and the effect of a voltage will be artificial since there is physical meaningful place for the voltage drop to be placed.
Title: Re: Calculation the transport properties of graphene
Post by: esp on January 16, 2012, 22:52
Why do you keep referring to my structure as metallic?  I created an AGNR which should be a semiconductor, and indeed I have checked and there is a significant bandgap ... also why 1d?  I make a nanoribbon, isnt that 2d?
Title: Re: Calculation the transport properties of graphene
Post by: esp on January 16, 2012, 22:56
also about "the box" ... i assume you are talking about the unit cell padding ... should i just make this arbitrarily large then?  Is there any information on this?  I am sorry i don't know what "the box" is ... I am guessing this is the region of calculation for various things, set by this unit cell padding parameter from the gui?
Title: Re: Calculation the transport properties of graphene
Post by: Anders Blom on January 16, 2012, 23:09
You are right, but metallic is not the point :) The point is that it's perfectly periodic. So, once you increase the bias large enough to make it overcome the bandgap, the semiconductor turns "metallic", and the same argument applies.
Title: Re: Calculation the transport properties of graphene
Post by: esp on January 16, 2012, 23:20
I see ok I just want to make sure I understand correctly. 

On the point of IV curves .. there are certainly many papers that report IV curves for what they term "perfect" GNRfet structures ... for example: http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=5567164&openedRefinements%3D*%26filter%3DAND%28NOT%284283010803%29%29%26searchField%3DSearch+All%26queryText%3DGraphene+Nanoribbon+FETs%3A+Technology+Exploration+for+Performance+and+Reliability (http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=5567164&openedRefinements%3D*%26filter%3DAND%28NOT%284283010803%29%29%26searchField%3DSearch+All%26queryText%3DGraphene+Nanoribbon+FETs%3A+Technology+Exploration+for+Performance+and+Reliability)

Now, you say that ATK considers the ballistic regime ... I am not sure if I understand well enough, but my understand was that electrons will only move ballistically if you do not consider higher order effects in the structure, like phone scattering, nearest neighbor interactions, etc ... are you saying there is a limitation in ATK that will not allow me to produce a plot like those in the paper, or is it that I am not in full understanding here ... ?

In other words, my understanding was that ATK can calculate IV curves at the most sophisticated level, including higher order interactions and effects .. is this the case?  Is it that the way I made it, my structure is too simplistic?

Title: Re: Calculation the transport properties of graphene
Post by: esp on January 17, 2012, 07:59
maybe my problem is that i have no introduced any doping so i have only one type of GNR, sorry i will revisit the structure
Title: Re: Calculation the transport properties of graphene
Post by: kstokbro on January 17, 2012, 10:02
ATK will include all elastic scattering effects, like scattering with a doping atom or other imperfections in the structure.

It will not include inelastic scattering effects, where the electron looses energy, like in the scattering with a phonon.
Title: Re: Calculation the transport properties of graphene
Post by: esp on January 17, 2012, 10:03
ok thank you