Transmission spectrum for GatedTwoProbeMethod

[lamkt]

Hi,

I'm having some problem understanding the transmission spectrum for GatedTwoProbe calculations.
I was expecting the transmission to be shifted along the energy axis by the same amount of bias that is applied but that doesn't seem to be the case.  Does defining the screening atoms have any effect on the transmission spectrum?

Rgds,
Dick

[Anders Blom]

The transmission will not be shifted. The purpose and effect of the applied gate "voltage" is to apply a shift to the diagonal Hamiltonian matrix elements for the atoms in the central region not designated as surface_atoms. This way one can mimic (I would not say simulate since we "simulate"=model the transport properties in a correct way) the effect of a third electrostatic gate on the transmission spectrum.

So, the screening atoms should be the ones not affected by the gate, according to the way you imagine the gate will influence the system.

This functionality is not entirely trivial to use, that is, one needs to be a bit careful with the interpretation of the results. It can however be put to very good use such as in Q. Yan et al., Nano Letters 7, 1469 (2007). Also you can search our publication list for the words "gating" and "gated" to find more inspiration.

Finally, QuantumWise is currently implementing a completely new model for simulating gates, which will allow for self-consistent electrostatic modeling metallic and electrostatic gates. This will make it possible to simulate nanoscale transistor structures in a much more realistic way.

[privador]

y and x axis are repleced comparing with tutorial example.Is it any problem?

[Anders Blom]

No.

(I think you will want to move this post, it seems to belong to a different thread or should be in a thread of its own.)

[lamkt]

Thank you Dr. Blom.  However, I still have some questions that I would like to clear about this issue.  Parden me if my understanding of NEGF is incorrect and appreciate you will point me to the correct path.

1)  Transmission under different gate biases.
If the transmission does not change under different gate biases, and if the chemical different between the two probe remains the same, how can the current be different?  I'm guessing that the chemical potential at the source and drain and also changed by the gate biases (in addition to the change in the device Hamiltonian) but I'm not sure how to varify that.

2) Screening length and gate biases.
I did a little experiment with Prof. Datta's codes in Quantum Transport and implemented the Vg similar to ATK (according to what I understand).  I found out that if my screening length is not sufficient, the transmission will be changed (not shifted, just some anormalies) if different gate biases are applied.  And this screening length requirement increases with larger biases (which make sense intuitively but I've yet to understand why).  Hence can I safely assumes that if and when I found anormalies in the transmission spectrum from ATK under gate biases, the first thing I should do is to increase the screen region? (I would actually want to try simulate this but my structure is already too big and the time taken to varify would be too long).

It would be great to have ATK implement the gate bias self-consistently.  However, I'm just wondering should I expect the transmission to shift by the same amount of the gate bias if it is implemented 'correctly' or maybe my understanding of transmission spectrum under gate bias is totally wrong?

[Anders Blom]

I was probably a bit unclear, I didn't mean that the transmission will not change, I just meant that it will not necessarily be a simple shift, there is a potentially complex self-consistent response in the density etc also to the Hamiltonian shift. You do however shift the molecular levels in the central Hamiltonian, so in the simplest picture, yes, the transmission spectrum will shift.

I think your analysis about the screening layers is very correct. Too few screening layers can often be a problem that may compromise the quality of the results. Indeed, larger screening is required for higher bias.

[lamkt]

Oh... So the transmission should change (but not just a simple shift) and the gate bias is only applied at the Hamiltonian (something like G=inv(E-H-Vg)) but not at the source and drain Fermi-Dirac distributions (f1,f2).  I had the impressions that Vg was applied at the (f1,f2) in the earlier versions of ATK and just want to be sure about the implementation and the results I got.

[Anders Blom]

Oh... So the transmission should change (but not just a simple shift) and the gate bias is only applied at the Hamiltonian (something like G=inv(E-H-Vg)) but not at the source and drain Fermi-Dirac distributions (f1,f2).

Exactly, but the gate voltage shift is only applied to the selected atoms.

I had the impressions that Vg was applied at the (f1,f2) in the earlier versions of ATK and just want to be sure about the implementation and the results I got.

The source/drain bias is applied by setting the electrode voltages. This shifts the Fermi levels of the leads with respect to each other. This is how it always has been