Author Topic: Gold simulation  (Read 6520 times)

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Offline gM

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Gold simulation
« on: July 10, 2012, 18:46 »
Hi all and thank you for your attention  ;).  I simulated the IV characteristics from (-0.3V to 0.3V) of three gold wires with dimensions:

Contact Length (z direction)          Width of wire (y direction)            Central region length (z direction)
8.16A                                                    20A                                             26.4A
8.16A                                                    20A                                             30.6A
8.16A                                                    20A                                             51.2A

For all three I used k-point sampling of 1,1,100 for left/right electrode accuracy.

The IV characteristics of all three structures look nearly identical when they should theoretically change slope as the resistance of a longer piece of metal should increase and hence less current should pass through. Would you be able to tell me what I may be doing wrong here?  I have attached the three scripts for the devices as well as the result I got.


Offline kstokbro

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Re: Gold simulation
« Reply #1 on: July 10, 2012, 22:41 »
For ballistic transport, the resistance is independent of the length of the wire, see forinstance
 Y. J. Lee, M. Brandbyge, M. J. Puska, J. Taylor, K. Stokbro, P. Ordejon, and  R. M. Niemenen. Electron transport through monovalent atomic wires, Phys. Rev. B 69, 125409 (2004).

Offline mads.engelund

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Re: Gold simulation
« Reply #2 on: July 11, 2012, 09:24 »
A nice piece of litterature: later M. Brandbyge was also involved in investigating non-ballistic transport in these wires.
T. Frederiksen, N. Lorente, M. Paulson and M. Brandbyge. From tunneling to contact: Inelastic signals in an atomic gold juntion from first principles. Phys. Rev. B. 75(23): 235441, 2007.

Offline Anders Blom

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Re: Gold simulation
« Reply #3 on: July 12, 2012, 14:27 »
The fact that the resistance of a nanoscale metallic conductor is independent of its length (and therefore "resistance" isn't the proper measure, but rather we use conductance) is the whole point of nanoelectronics, in a sense. I recommend reading some of the books by Datta on the topic.

But it's nice to see that you actually get that result when doing the simulation, it proves the methods are correctly implemented 8)

Offline gM

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Re: Gold simulation
« Reply #4 on: July 12, 2012, 21:39 »
Thank you for your response. I was looking at conductance = dI/dV which is the inverse of resistance.  Both should change with length and width because ballistic transport doesn't seem to dominate even in 5nm devices such as MOSFETs which are routinely fabricated. Is this an artifact of some approximation where you assume the lattice is infinite along that direction that's why the simulation results don't change with length?

Invoking theory rather than experiment to support the accuracy of your program is not reassuring. The program simply solves numerically a set of theoretical equations.  According to you, what should be the length of gold wire beyond which non-ballistic behaviour (standard observed experimental behaviour) occurs (5nm, 10nm 100nm)? Can this program simulate that? Do you expect that the conductance should change with width of the wire at these dimensions?

Your answer so far does not give me confidence that this program can be used to simulate practical 5-10nm transistors which many academic and industrial labs have demonstrated experimentally to behave classically like 1um long devices.

I have attached the conductance plot of the above mentioned gold wires.

Offline Anders Blom

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Re: Gold simulation
« Reply #5 on: July 13, 2012, 12:11 »
The reason for invoking theory is that it's crucial to understand within which theoretical framework a software package operates. Sure, we solve the numerical equations as exactly as possible, but the equations themselves are set up under certain assumptions, since it's impossible to solve the full quantum-mechanical problem for a system of more than 1 or 2 atoms. This is no different from a macroscopic device simulator which perhaps assumes a constant resistance, or parabolic bands, etc, which may not hold for hot electrons or when dimensions are reduced, etc.

In the case of ATK, one of these assumptions is the absence of inelastic scattering, e.g. in the shape of phonons, or any phase decoherence. That is, we solve the problem in the coherent, ballistic regime. It may certainly be the case that phonons etc will limit the mobility of a realistic device, and you may also not have the exact same geometrical configuration in each fabricated device (small fluctuations, random dopants, etc), but what ATK is designed to do is to provide a theoretical limit to the performance of the device, and to give some picture of the variability (you can insert randomness explicitly and see how it affects the conductance or not). ATK is also intended as a tool to make choices between possible design choices, to judge which one will likely be the better candidate, before making an expensive experiment, and finally to provide insight into the mechanisms that control the device operation. If these are understood on a fundamental level, you have a better chance to optimize the design or come up with ideas for new and improved device configurations.

Offline gM

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Re: Gold simulation
« Reply #6 on: July 20, 2012, 23:34 »
Thank you for your informative response.  I would like to pose a few more questions:

1. So, should I expect any change if I were to simulate a structure similar to the one simulated only 10nm long? Why / why not?

2. What exactly are dielectric / metallic regions in terms of this program?  If I were to build a metallic region with ATK and set a certain voltage on it, near a gold wire (with dielectric in between), how does it impact the conductance in the gold wire?

3. How do I determine which way the electric field from that metallic region is facing? Is it "away from the metallic region" when positive voltage is applied, and "towards the metallic region" when negative voltage is applied (treatment of electric field due to infinite charged sheet)?

4. What parameters do I need to adjust in the calculator in order to be able to simulate with metallic/dielectric regions? (I've come across changing the Poisson solver to have a Neumann boundary condition instead of Periodic on this forum) Would you be able to elaborate here?

5. Will an influence of a strong electric field, enhance/degrade the transport in the channel under ballistic regime?

Offline Anders Blom

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Re: Gold simulation
« Reply #7 on: July 25, 2012, 14:04 »
I have now had a chance to look at your structure a bit more carefully. First of all, the ballistic transport characteristics of a perfectly periodic 1D structure are not very interesting, and you don't really need to do such an elaborate calculation at all, you can just look at the band structure to determine the transmission spectrum - at least at zero bias. However, your structure isn't really a wire, it's actually an infinite 2D gold sheet. In that case, since it's still perfectly periodic, you can again get the results very quickly from the bulk structure, as described in http://quantumwise.com/publications/tutorials/mini-tutorials/167.

Also note that your system is repeated periodically in the X direction which only makes the calculation take longer time without changing the results. You will however need to introduce k-points in A if you use the minimal cell instead, but k-points scale linearly (and parallelize) while atoms scale as N^3.

Now, in regards to your questions:

1. As long as the system is perfectly periodic, the ballistic conductance is independent of the length of the system.

2. These regions are used to simulate gates and dielectric materials inserted into the device. So, introducing a metallic region will have the same (at least similar) effect as a real gate electrode.

3. Just like normal electrostatics.

4. You should use the multigrid solver. The discussion at http://quantumwise.com/forum/index.php?topic=1597.msg8224 is very enlightening, I hope.

5. That's for you to investigate before the question can be answered :)




Offline gM

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Re: Gold simulation
« Reply #8 on: July 25, 2012, 15:45 »
Thank you Dr. Blom for your quick response. Perhaps I'm not setting my system up correctly.  As noted above I'd like to setup a gold nanowire with certain width/length/height.  As I understand correctly, the program looks at the periodicity in the C direction around the edges of my "bulk configuration" and duplicates that several times to create electrodes which extend infinitely (in the C direction only) approximating bulk properties at both ends.  But, the X and Y dimensions in the central region, and electrodes should be limited to the width/height of the wire without extending further (infinitely periodic in those directions). How do I achieve exactly that?

Thanks again :)!

Offline Anders Blom

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Re: Gold simulation
« Reply #9 on: July 25, 2012, 15:54 »
Quite simply by adding vacuum. So if you take your system to the Builder, and open Bulk Tools>Lattice Parameters, then change the X-component of the A vector to twice its current value, you will obtain a (flat) wire. In that case the 1x1 k-point sampling is correct.

Offline gM

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Re: Gold simulation
« Reply #10 on: July 25, 2012, 17:55 »
Thanks Dr. Blom.  Is it necessary for the x-component to by twice its current value or just a little bigger is fine as long as the bonds of the end atoms do not show anymore? Referring to the attached, is there any difference between simulating B or C, except the fact that C has more vacuum in the X direction?

Offline Anders Blom

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Re: Gold simulation
« Reply #11 on: July 25, 2012, 23:00 »
No, 2x was just a rough measure, based on how your structure looks. You can probably do with a bit less, but just looking when the bonds stop forming is not really enough, since the electrostatic interactions (and basis sets) reach farther than the bonds. But the vacuum is not so expensive, so I would go with "C", your "B" looks too tight for comfort.