Transport calculation direction

[Bobby]

As mentioned in the tutorials, the transport is only calculated in the Z direction. Does that mean the electrodes (left and right) should always have the same coordinates (in x and y directions) ?

I mean, for example, for the configuration below, is it possible to calculate its transport spectrum and I-V curves. etc with ATK?


----------------------> Z-direction
                                                                                                 X (or Y)-direction
(hhhhhhhhhhhhhhhhhhh)  hhhhhhhhhhhhhhhhhhhhhhh                                             /\
(hhhhhhhhhhhhhhhhhhh)  hhhhhhhhhhhhhhhhhhhhhhh                                              |
(hhhhhhhhhhhhhhhhhhh)  hhhhhhhhhhhhhhhhhhhhhhh                                              |   
                                   hhhhhhhhhhhhhhhhhhhhhhh   (hhhhhhhhhhhhhhhhhhhhhh)     |
     Left electrode           hhhhhhhhhhhhhhhhhhhhhhh   (hhhhhhhhhhhhhhhhhhhhhh)     |
                                   hhhhhhhhhhhhhhhhhhhhhhh   (hhhhhhhhhhhhhhhhhhhhhh)     |
                                       
                                           Center region                     right electrode

Really need to know this and thanks in advance.

Best

[Anders Blom]

Yes, ATK can treat this situation of heterogeneous electrodes. In fact, the electrodes can also be made of different materials. The only requirement is that the total simulation cell in the XY plane is the same for the two electrodes and the central cell. This seems trivial to achieve in your case, as you just need to add vacuum around, but if the two electrodes are for instance different bulk materials with different lattice constants, one (or both) need to be strained a bit to fit.

[Bobby]

Dear Anders,

Thanks for your reply. In fact, I would like to use the heterogeneous electrodes configuration because I want to apply bias voltage on the central region (see below), The dielectric will be covered on part of the surface of central region. Can ATK simulate the transport of this configuration?

If so, how should I set the cell size of electrodes, central region and dielectric?

Thanks


----------------------> Z-direction
                                                                                                                                     X-direction
(hhhhhhhhhhhhhhhhhhh)  hhhhhhhhhhhhhhhhhhhhhhh   ********************   <-(bias-voltage)    /\
(hhhhhhhhhhhhhhhhhhh)  hhhhhhhhhhhhhhhhhhhhhhh   ****     dielectric     ****   <-(bias-voltage)    |
(hhhhhhhhhhhhhhhhhhh)  hhhhhhhhhhhhhhhhhhhhhhh   ********************   <-(bias-voltage)   |   
                                   hhhhhhhhhhhhhhhhhhhhhhh   (hhhhhhhhhhhhhhhhhhhhhh)                           |
     Left electrode           hhhhhhhhhhhhhhhhhhhhhhh   (hhhhhhhhhhhhhhhhhhhhhh)                           |
                                   hhhhhhhhhhhhhhhhhhhhhhh   (hhhhhhhhhhhhhhhhhhhhhh)                           | 
                                       
                                           Center region                     right electrode

[Anders Blom]

A bias voltage by itself doesn't make sense, since there must be a reference terminal as well. Unless you are talking about a gate, but in that case the question still becomes, what are source and drain?

Also physically, you would never be able to separate a gate gap that only acts on the dielectric and not the hhhh atoms in the right electrode.

So, please consider what you really want to simulate - and since you ask about "transport", do indicate source and drain as well.

Or maybe I just didn't understand your drawing... You said "bias voltage on central region", which I would understand as a gate, which is consistent with your "bias voltage" arrows, but then the picture should be

----------------------> Z-direction
                                                                                                                                     X-direction
                                     |      (bias-voltage)      |
                                     v                               v
                                   ********************   
                                   ****     dielectric     ****   
                                   ********************
(hhhhhhhhhhhhhhhhhhh)  hhhhhhhhhhhhhhhhhhhhhhh                                            /\
(hhhhhhhhhhhhhhhhhhh)  hhhhhhhhhhhhhhhhhhhhhhh                                             |
(hhhhhhhhhhhhhhhhhhh)  hhhhhhhhhhhhhhhhhhhhhhh                                             |   
                                   hhhhhhhhhhhhhhhhhhhhhhh   (hhhhhhhhhhhhhhhhhhhhhh)    |
     Left electrode           hhhhhhhhhhhhhhhhhhhhhhh   (hhhhhhhhhhhhhhhhhhhhhh)    |
                                   hhhhhhhhhhhhhhhhhhhhhhh   (hhhhhhhhhhhhhhhhhhhhhh)    |
                                       
                                           Center region                     right electrode

If that's what you mean, then the answer is a clear "yes", ATK can treat this; in fact, it's basically identical in nature to http://quantumwise.com/documents/tutorials/latest/GrapheneDevice/index.html/.

[Bobby]

Sorry Anders, I guess I didn't make it clear. In fact, I would like to study the effect of bias voltage on the schottky barrier between graphene and doped-silicon (please see the picture below). I would like to simulate the I-V characteristics of this configuration under different bias voltage.


----------------------> x (or y) -direction
                                                                                                                                     
                                                                                                                                                                                                                                                                                                                         
                                     | (gate: bias-voltage) |
                                     v                             v      (electrode:source)
                                   ********************   eeeeeeeeeeeeeeee
                                   ****     dielectric    ****    eeeeeeeeeeeeeeee       
                                   ********************   eeeeeeeeeeeeeeee               
                                  GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG                                          /\
                                  GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG  (G:Graphene)                       |
     (schottky barrier)      GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG                                          |    Z-direction
                                   ssssssssssssssssssssssssss                                                                        |
                                   ssssssssssssssssssssssssss      (s: doped-silicon)                                          |
                                   ssssssssssssssssssssssssss                                                                        |
                                   eeeeeeeeeeeeeeeeeeeeeee
                                   eeeeeeeeeeeeeeeeeeeeeee           
                                   eeeeeeeeeeeeeeeeeeeeeee
                                          (electrode:drain)

[Anders Blom]

I think I'm starting to understand it, but at the same time I would then expect your electrodes in the x (or y) direction to be very large (macroscopic). Therefore, what might make more sense is


----------------------> z direction

                          | (gate: bias-voltage) |
                          v                      v     
                           ********************     eeeeeeeeeeeeeeee  (electrode:source)
                           ****  dielectric ***     eeeeeeeeeeeeeeee       
                           ********************     eeeeeeeeeeeeeeee               
                          GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG                      /\
                          GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG  (G:Graphene)        |
  (electrode:drain)       GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG                      |    X direction
                          ssssssssssssssssssssssssss                                      |
                          ssssssssssssssssssssssssss       (s: doped-silicon)             |
                          ssssssssssssssssssssssssss                                      |
                          eeeeeeeeeeeeeeeeeeeeeeeees
                          eeeeeeeeeeeeeeeeeeeeeeeees         
                          eeeeeeeeeeeeeeeeeeeeeeeees
 

The primary difference is that the electron current now comes in from the left (or right) in this picture, in an electrode consisting of a thin "e" with thin "s" on top, plus "G", extending infinitely to the left (-Z), then using the graphene to transfer over to the right part, and exiting (or opposite - depending on s-d bias direction) through the right electrode.

The graphene could cover the electrodes or be finite in the middle.

[Anders Blom]

I guess you could use your picture too, but in that case the transport direction is across the graphene layers, so you have to trust the very weak pi-bonds to carry the current, and that will not give much to work with.

[Bobby]

Thanks Anders. I got your idea. Just one more confusion:

Since the aim of my work is to study the electron transport through the schottky barrier (between graphene and "s:doped-silicon") under different bias voltages, which means the electron should transport across the graphene layer.

However, as shown in your configuration:

                                           the left electrode consists of  a thin "e" with thin "s" on top, plus "G"
                                           right electrode includes "G" and thin "e" on the top
                                           central region is filled with graphene

Thus, when we calculate its I-V characteristics, it seems only the electron transport along the graphene layer is taken into consideration. To my understanding, this has no difference with the structure with only graphene in the whole device (please see the picture below)


----------------------> z direction

                          | (gate: bias-voltage) |
                          v                             v     
                           ********************     
                           ****      dielectric     ***                   
                           ********************                  (electrode:source)         
                          GGGGGGGGGGGGGGGGGGGGG  GGGGGGG  GGGGGGGGGGGGGG            /\
                          GGGGGGGGGGGGGGGGGGGGG  GGGGGGG  GGGGGGGGGGGGGG            |
  (electrode:drain)  GGGGGGGGGGGGGGGGGGGGG  GGGGGGG  GGGGGGGGGGGGGG            |
                                                                                                                      |    X direction
                                                              (Central region)

[Bobby]

Hello anders,

what do you think about my confusion above?

Looking forward to your reply. Thanks

Best

[Anders Blom]

You are right, I thought of this after I answered. It is in principle possible to make the graphene finite, and not be part of the electrodes, but that's perhaps still a different system than you had in mind. On the other hand it's hard to picture exactly how your Schottky barrier is formed - if the graphene is flat in the Si, then you would have transport across graphene layers, which is only very weakly conducting, whereas if you want to do something where the graphene is on top of the metal you are more in the situation of doi:10.1103/PhysRevB.85.165442. Or somewhere in between - I think we need a better picture (and perhaps ASCII drawings is not the best tool for getting the point across ).

[Bobby]

Thanks for your reply, Anders.

I have read your paper: doi:10.1103/PhysRevB.85.165442 .

I think the configuration I would like simulate is very similar to the nickel-graphene case (just need to replace the nickel atoms with doped-silicon, and add a vertical gate bias on the interface of nickel and graphene).

If you still do not understand what the configuration is, please have a look at this paper:

[ J. Chauhan, A. Rinzler, and J. Guo, "A Computational Study of Graphene Silicon Contact", J. Appl. Phys., vol. 112, p. 104502, 2012. ]

Download address: http://scitation.aip.org/content/aip/journal/jap/112/10/10.1063/1.4759152

The gated graphene-doped_silicon contact presented in it is exactly what I would like to study with ATK.

I hope all your confusions should be clear in it and I am looking forward to your suggestions.

Best

[Anders Blom]

The simulation in this paper is done with effective mass theory, so they are able to treat the entire gate stack which is about 100 nm long. That would be very hard to do atomistically, although it's possible provided the lattice constant matching is very good between all regions.

But the relevant effect you are looking for is (?) Schottky barrier height modification as a function of bias at the Si|graphene interface. This can be modeled simpler, without necessarily setting up the full stack. You could just make an interface like we did for Ni-graphene and focus on that part of the device.