Electrodes highlighted in red/Repetition score

[chrsop]

Greetings

I am investigating symmetric TiN / metal-oxide / TiN devices (that is Titanium-Nitride, not the element Sn) and am scratching my head over the electrode and scattering region sizes. I will refer to electrode/system sizes in terms of layers of TiN (2 layers is approximately 4.25Å). The scattering region has been relaxed with respect to two TiN layers on either side of the dielectric (and some of the dielectric layers). Hence, these TiN layers no longer have a bulk-like structure.

When setting up a device, choosing 6 TiN layers/side lets me choose a 2-layer electrode with a repetition score (RS) of 0. Choosing 8 TiN layers/side lets me choose between a 2-layer electrode with RS +16  or a 4-layer electrode with RS -16. The length of the 4-layer electrode is highlighted in red. If I opt for a 10-layer electrode, I can choose 2 layers (RS +32), 4 layers (RS 0) or 6 layers (RS-32, highlighted in red).

1) I interpret the red highlight as a warning signal related to the electrode size relative to the device size. What, specifically, is the problem? To be clear: I see this when the scattering region size is a total 8 TiN layers on either side of the metal-oxide. Of these 8 layers, the 2 interface layers are relaxed, leaving 6 bulk-like TiN layers.

2) In another post (https://quantumwise.com/forum/index.php?topic=3862.msg17625#msg17625), the meaning of the repetition score was touched upon. Supreme ATK Wizard Anders Blom explains "[...] generally, a negative score is good, so if you don't see any negative score at all in the list, you should be careful and think why." When I increase my scattering region size, the electrode repetition score increases as well (from 0 -> 16 -> 32 for the 2-layer electrode). Is this bad news, or how should I interpret this?

3) I have simulated a device consisting exclusively of intrinsic TiN (16 layers in the scattering region). When using short, 2-layer electrodes, the Hartree potential shows odd peaks at the first and last layers (see attachment). When using long, 4-layer electrodes, I do not get these peaks. I have previously seen these peaks for my TiN/M-O/TiN devices with short electrodes, which is why I did the calculation of intrinsic TiN to check. Do you know what is going on here? Is it just that a 4.25Å electrode is too short?

Attachments:
TiN_device.py (intrinsic TiN device script with 4-layer electrodes)
TiN_short_device.py (intrinsic TiN device script with 2-layer electrodes)
TiN-Al2O3-TiN.py (Structure file of the junction I want to set up as a device)
UH_short.png (Python plot of the Hartree potential of the short TiN device)

I run VNL 2017.1 locally, with VNL/ATK 2017.0 for actual calculations.

Kind regards
Christian

[Ulrik G. Vej-Hansen]

The short answer is that yes, an electrode of 4.25 Å is probably too short. You can check it in VNL by first doing an SCF calculation of just the electrode, and then using the "Electrode Validator" tool in the VNL panel on the right.

The repetition score is maybe a little more complicated than necessary, as there is only really two criteria for the length of an electrode:

1. It should be so long that there is no interaction between an atom and its periodic image in the c-direction. A good rule of thumb to achieve this is that the length of the electrode should be at least twice the length of the longest basis function in the basis set.  This criteria is the one checked by the electrode validator.

2. It should be no longer than absolutely necessary to fulfill 1.

With regard to your central region, be aware that it the first electrode-like unit is known as the electrode extension, and must be kept fixed. So your central region should be long enough to fulfill this, and still allow any relevant relaxation etc. at the interface between TiN and the metal oxide.

[chrsop]

I thank you for this elaboration. Looking at the basis for Ti, the longest cutoff radius is 4.264 Angstrom, whereas for Nitrogen it is 4.609 Ang. My four-layer electrode is 8.507 Angstrom and thus violates criterium 1) with ~0.7 Angstrom.

So I have three options: reduce the cutoff radius by ~10%, increase the electrode size to 12.761 Angstrom, or just ignore it (depending on the rigidity of this rule of thumb). Which do you suggest?

I have a last question about the aforementioned peaks in the Hartree difference potential. Moving to a system size of 12 TiN layers helped convergence and gave nice Hartree difference potentials. However, for one system, adding a small bias (+/- 0.1 V) resulted in a peak for the right electrode - see attached files. In both cases the bias was applied to the left electrode. Any idea as to the origin of this effect?

[Ulrik G. Vej-Hansen]

Increase the length of the electrode is always the recommendation in this case. Changing the basis functions is in general a bad idea unless you know exactly what you are doing.

My best guess is that your system is only just long enough to screen the electrodes under zero bias, but not under finite bias. Note that we recommend distributing the bias evenly, for numerical reasons. In your case that would be 0.05 V and -0.05 V instead. I would also suggest using longer TiN regions. We will also very soon, probably later today, publish a guide on convergence of NEGF calculations, which also explains some of the pitfalls of device construction in more detail than we can do here. It will become available here: https://docs.quantumwise.com/technicalnotes/negf_convergence_guide/negf_convergence_guide.html