The effect of bias on transport property?

[chp]

    Recently, I performed some test calculations bout the effects of the applied bias on the transport properties of graphenen nanoribbons. The attached figure shows the results of two kinds of armchair nanoribbons. It can be seen that in both of cases, with the increase of bias, the transport spectra move further away from the Fermi level as well as the suppressed amplitude for a wide range of energies. At higher bias voltage, there are nonzero transmission values near the Fermi level in the original band gap, the transmission values of which are dependent on the bias voltage. Where do the nonzero transmission values in the original band gap come from? How to understand these phenomena?

    Thanks in advance!

[nori]

Where do the nonzero transmission values in the original band gap come from? How to understand these phenomena?

It's a band-to-band tunneling from a valence band to a conduction band.

on the other hand,

the transport spectra move further away from the Fermi level as well as the suppressed amplitude for a wide range of energies.

"the suppressed amplitude" comes from breaking the periodicity of effective potential by applying bias voltage and mismatch of Bloch States.
"move further away" is due to the shift of Fermi-level of electrodes.
In order to have finite transmission coefficient at some energies in coherent transport, there should be DOS in electrodes and central region simultaneously at the same energy.

[camelluxin]

But can we get the DOS and bandstructure of electrodes by ATK?

[nori]

But can we get the DOS and bandstructure of electrodes by ATK?

Electrodes are defined as Bulk system, that's why it can be easily done

[chp]

Thanks.

I also calculated the projected density of states (PDOS) of C atoms in the central region. (please see the attached figure.) Figure (a) shows the transmission spectrum and the PDOS of a graphene nanoribbon. It can be seen that there is a region of zero transmission located around the Fermi level, the width of which coincides with the energy gap in the plot of PDOS. However, at the bias voltage of 1.5 V (figure (b)), there are nonzero transmission values near the Fermi level in the original band gap, while the gap in the plot of PDOS disappears and there is a continuous distribution of DOS in the whole range of energies. I want to know whether the finite DOS near the Fermi level is only due to the band-to-band tunneling from a valence band to a conduction band. Why is the PDOS continuous in the whole energy scale? Furthermore, figures (c) and (d) show the cases of a locally deformed graphene nanoribbon. It is noteworthy that there are obvious electron states near the Fermi level in the plot of PDOS under a bias voltage of 1.5 V. Why is the shape of the PDOS near the Fermi level fluctuant? How to analyses and understand this phenomenon?

Thanks in advance!

[kstokbro]

To get a finite transmission a energy E, you need states in both electrodes at energy E, because the electron must propagate from one electrode  into the central region and out to the other electrode.

To get a finite DOS at energy E, you only needs states in one of the electrodes at energy E, because the electron only needs to propagate from one electrode into the central region.

Thus, you can easily have a finite dos but zero transmission at a given energy E.

[chp]

Thank you for your reply!

Can we calculate the PDOS of the left/right electrode under a finite bias voltage in ATK 2008.10 using a function like the following example or other methods?

http://quantumwise.com/forum/index.php?topic=69.msg338#msg338

[kstokbro]

I recommend that you upgrade to the latest version ATK11.8, it has the pdos functionality and you can calculate the pdos very easily using VNL.

[chp]

Thank you very much!