Inconsistency in the current analysis for InelasticTransmissionSpectrum

[weixiang]

Hello,
From the Inelastic Transmission Spectrum Analyzer I got the I-V curve (attached image.png) for 0-0.2V bias voltage and it can be noted that at bias = 0.2V the sum current (elastic current, inelastic current as well) is of ~10^-22 A = 10^-13 nA
However, I also generate its corresponding spectral current at 0.2V.(attached image-1.png), it can be approximated from the area under the curve that the current is ~10^-14  A= 10^-5 nA.
These two currents are supposed to be same with each other, but now they are 8 order of magnitude different.
Why is the case? Is this a bug in ATK?

Please check my attached scripts, I wonder if there is anything wrong in my calculation procedure.

Thank you! Any help is appreciated!

[weixiang]

Attached is the involved dynamic matrix and Hamiltonian Derivative scripts for calculating the InelasticTranmissionSpectrum.
I can not attach all my files in one time.

Thanks!

[Daniele Stradi]

Dear Weixiang,

It makes good sense to me. The peak in the spectral current lies outside the bias window that you have considered for the inelastic transmission spectrum. When you calculate the current at 0.2 V, the total current is obtained by integrating the spectral current between -0.1 V and 0.1 V.

Daniele

[weixiang]

Thanks for the reply!
But the peak at -0.5 eV is also contributing to the total current, but why not take it into the integral? Instead, only the bias window (-0.1eV,0.1eV) is considered?
What I understand is that due to the phonon-assisted band-to-band tunneling effect, the tunneling at -0.5 eV is largely increased compared to the non-interacting case, and thus created a peak of 10^-5 nA in the spectral current.
In calculating the total current from the spectral current why don't we integral over all energy range to get a more accurate result?

Thanks!

[weixiang]

And as a result of  only integrating over only the bias window (-0.1ev, 0.1ev) , what is the true total current?  The one of ~10^-13 nA, or the one of ~ 10^-5 nA?
Does such difference mean there is strong phonon-assisted band-to-band tunneling occurred outside the bias window?

[Petr Khomyakov]

The correctly calculated total current is that given by the Inelastic Transmission Spectrum Analyzer, ~10^-13 nA. 

[weixiang]

Thank you for the reply!
But can you give me a little more details?
Why only the bias window (-0.1eV,0.1eV) is considered in calculating the total current?

Thanks!

[Petr Khomyakov]

Why only the bias window (-0.1eV,0.1eV) is considered in calculating the total current?

Please read some textbooks on the electron transport, e.g.,  by S. Datta, https://books.google.de/books?id=BlYhAwAAQBAJ&lr=. Taking a look at the reference papers given in the manual https://docs.quantumwise.com/manual/Types/InelasticTransmissionSpectrum/InelasticTransmissionSpectrum.html might also be of help.

[weixiang]

Thank you for the reply!
I think I have got the answer.
"In situations where there are no electrode states at the Fermi energy, like in a low- or un-doped semiconductor, the direct use of the LOE and XLOE expressions will result in zero inelastic currents, when evaluated at the Fermi energy. In that case, the inelastic transmission spectra must be calculated at a range of energies (like the normal TransmissionSpectrum). The current can then be calculated as:

bias = numpy.linspace(-0.1,0.1,100)*Volt
current = inelastic_transmission_spectrum.inelasticCurrentIntegral(bias=bias)"