Author Topic: What's the difference among the three concepts about DensityofStates?  (Read 4371 times)

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Offline lknife

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Dear experts,

I have been using ATK for nearly a year but I am still confused about these three concepts: DeviceDensityofStates, LocalDeviceDensityofStates and ProjectedLocalDensityofStates. Can anyone give me a simplified explanation about the difference among them?

Thank you very much for your kind help!

Offline Jess Wellendorff

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This is a very good question (might actually consider it for a future online tutorial or something similar). Let me explain as plainly as possible:

As an example, I have run a fast device calculation for a carbon nanoribbon, and have done the DDOS, LDDOS, and PLDOS analyses in order to compare them. I also attach 4 images (A, B, C, D).

DeviceDOS: Image A. This is the device equivalent of ordinary density of states. The main difference from ordinary DOS (for bulks) is that spill-in terms from the electrodes must be taken into account. As the images shows, the DDOS results in a plot of the DOS against electron energy, just as with ordinary DOS, so the is no spatial information in the DDOS (i.e. "where in the system is the DOS large/small?") - we only know the total device DOS vs. energies, not vs. position.

LocalDeviceDOS: Images B and C. The LDDOS gives you the spatial information that is not included in the DDOS. The local DOS is simply calculated in small volume elements throughout all of the device central region. This gives you a GridValues type object which can be visualized in 3D real space using the Viewer. As you see in the images (B: cutplane, C: density), the LDDOS gives you the energy-dependent DDOS in real-space volume elements. (You may use the 1D Projector to get 2D plots, but that's not the point here).

ProjectedLocalDOS: The PLDOS simply takes the LDDOS and projects it onto the Z-axis of the device. This makes it possible to plot a contour plot of the energy-dependent DOS along the device transport direction. So the plot has energy and z-position on the axes, and the numerical value of the DOS is represented by contours.

I hope this makes sense. Thanks for asking an excellent question.
- Jess

Offline Jess Wellendorff

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... and here are the remaining attachments.

Offline lknife

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Thank you for your elaborate explanation. It really helps!

I also want to know, what the difference of these three concepts in terms of time consuming for a calculation.  If there is the case that one of the three concepts can represent the other two? In other words, if one of them has been calculated (maybe with the most time consuming), there's no need to calculate the other two? Or what's the criterion for selecting the one to be calculated?

Thank you very much again for your help!
« Last Edit: July 26, 2017, 21:08 by lknife »

Offline Jess Wellendorff

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Ordinary DDOS will usually be fastest, but the PLDOS would usually be the scientifically most interesting. LDDOS and PLDOS will be the same time-wise, but I would in general recommend PLDOS.

Offline lknife

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Thank you very much for your kind help! Hoping to learn more from you in the future!

Offline Anders Blom

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The LDDOS is typically a lot slower because you need to compute it for each energy point, whereas the DDOS provides the results for all energies at once. Also, we can actually project the DDOS onto real-space in an approximate way, by projecting onto atoms (or layers), so this is a quick way to get a band diagram in e.g. metal-semiconductor junctions.

Offline lknife

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Thank you very much for your explanation. Could you please give me a detailed description of what you said? How to "project the DDOS onto real-space in an approximate way"?

Thank you again for your kind help! I am really suffering from the very long time-consuming for the calculation of devices now. I do want to have the band diagram in a Metal-semiconductor junction. I calculated the PLDOS of the device for this purpose which is very time consuming and I would like to speed it up.
« Last Edit: July 30, 2017, 13:29 by lknife »