Calculation using STD method cannot get converged

[weixiang]

Dear Sir,
I am studying the the inelastic current of a graphene nanoribbon Based TFET device using the STD method.

 I have read through the case studyhttps://docs.quantumwise.com/casestudies/std_transport/std_transport.html on Si device and trying to do the same thing on a GNR based device. So basically I  first computed the dynamic matrix of my device (GNR_PN_dynmat.py), then I computed the corresponding std configuration of my device (std-300k.py), next I started a loop to calculate the DeviceConfiguration at different bias voltage(300K_iv_scf.py), finally I calculated the transmission spectrum at these bias voltage (300K_transmission.py). The procedure is same as shown in the case study. The only difference is that I used a different forcefield potential Tersoff_CH_2010, since the materials is carbon rather than Silicon. And I used the Extended Huckel calculator rather than the DFT-LCAO calculator to calculated the DeviceConfiguration and transmission spectrum.
But the hard part is that the DeviceConfiguration calculation is very difficult to get converged.  Actually most of them did not converged at the max step. As a result the calculated current is oscillating wildly, making it hard to interpret:

The result is very unreasonable to me, and I don't know if it is solely due to the unconverged calculation.
So, can any one help me with:
(1)  why is the STD calculation so hard to get converged, and is there any specific advice for increase the convergence chance for my device calculation?
(2) If the calculation converged at all bias points will the oscillation diminishes, and the current curve looks more reasonable?

[weixiang]

I suspect that the width mismatch of the GNR at left/right electrodes may be one possible reason that cause difficulty in convergence (the reason for using a wider GNR for electrodes is that AGNR of such width is nearly metallic, while a narrower one in the central region is semi-conductive).
So I did the noninteracting (without considering e-ph interaction) calculation for the same device iv_scan_300k_pristine.py. And  I found out even for noninteracting calculation the convergence is still hard. The negative bias half all failed to converge and the calculated current at the negative region shows remarkable oscillation, which I believe is wrongly calculated..


I don't know if my suspect is reasonable or not. But that is what I thought. Any comment or advice is appreciated!

[Daniele Stradi]

Hi,

As explained in the reference paper, Phys. Rev. B 96, 161404(R) (2017), the STD method is supposed to work well only for systems that are periodic in the C direction, unlike the one that you are investigating.

Regarding the STD simulations, I would suggest to have a look at the projected local density of states to check if there are narrow resonances in the density of states, which could often result in convergence problems at finite bias voltages.  Also, notice that you cannot use the Huckel method for STD simulations.

I would also suggest that you first try to solve the problem with the non-STD device, which is more likely related to lack of screening in the electrode regions at finite-bias voltages.

Best regards,
Daniele

[weixiang]

Thanks for your reply! For non-STD device, do you mean the non-interacting case? And for lack of screening in the electrode region, can I solve it by increase the electrode length? But by how much? How do I decide?
More importantly, why the Huckel method cannot be applied to STD simulations? Is there any other available method other than the DFT method? (which could be very computationally expensive for this device) For example, like the  ATK-SE Slater-Koster?

Best regards!

[Jess Wellendorff]

Yes, non-STD means in this case non-interacting.
No, improved screening towards the electrodes are accomplished by (1) increasing the central region size and/or (2) doping the device.
The STD method relies in the dynamical matrix, so the simulation engine must provide reliable forces. Tight-binding models are in general not suited for this. On the other hand, classical force fields, as implement in the ATK-ForceField calculator, are idel for the purpose (i.e. for computing the dynamical matrix), provided that a good force field exists for the system of interest. I believe this is the case for a graphene-based device.