'constraint DensityMatrix' for Voltage drop

[jjhskang]

In the past question, I found that I need to use 'constraint DensityMatrix' means for the voltage drop calculation.
I do not know what it means.

(1) How and where do I use the new "constraint DensityMatrix" to calculate potential drop? Can anyone give me an example of the python script for it ? In which ATK command is it used?

(2)  Do I also need to use the 'constraint DensityMatrix' to calculate the effective potential itself ?

Thanks!

[jjhskang]

One more question:

Do I always need to center the system (both electrode and scattering region) at the center of X and Y coordinate for a correct two probe calcullation?

Does it make a problem if the system is near one border or corner of X and Y ranges?

Thanks!

[Anders Blom]

The whole business of the constraints is rather complex, I'm afraid. We're trying to clean it up to have only one in the future (one that works in all cases and is always correct!). About centering the coordinates, this is crucially important for the "RealSpaceDensity" constraint, but doesn't seem to matter for the other ones. Actually, if you center the coordinates, the "RealSpaceDensity" constraint is quite a good choice often. To use "DensityMatrix", you need to edit the script by hand, and enter it into the segment which normally looks like

Code

two_probe_algorithm_parameters = twoProbeAlgorithmParameters(
    electrode_constraint = ElectrodeConstraints.Off,
    initial_density_type = InitialDensityType.NeutralAtom
)

Here, set

Code

electrode_constraint = ElectrodeConstraints.DensityMatrix,

The Off constraint does not produce a physically correct effective potential (even if you are not going to take the difference).

[jjhskang]

Hi!

Thanks for your reply.

In fact, I found that the use of Desnitymatrix gives different I-V relationship. For example,

----------------------------------------
           electrode_constraint
           ---------------    ----------------
 bias      off                        Densitymatrix
------------------------------------------
0.1V   1.99e-07 (Ampere)     1.38e-07 (Ampere)
0.2V   3.32e-07  (" ")           1.86e-07 (")
------------------------------------------

As you can see from the above table, two different choices of electrode_constraint give different I(V) vs. V relation !!
Do you mean that only 'Densitymatrix' give correct results, and the use of default setting for the electrode_constraint results in incorrect results??

Thanks !

[Anders Blom]

It's hard to say without a detailed analysis of the effective potential profile, but the assumption is that both methods should give equal results if you have sufficient screening.

The DensityMatrix method does require, however, more screening layers, and so if you have too few surface layers, this could explain the difference.

Poor screening should show up as sharp jumps in the effective potential near the electrodes, or otherwise a bad potential profile along z.

[jjhskang]

Hi!

For my calculation, there is a small but nonnegligible jump in the Veff(z) vs z at the scattering region-electrode boundary, which means that I do not have sufficient layers of electrode in the scattering region. According to what you said, therefore, 'Off' constraint seems to be more reliable in this case. (Correct? ) What is strange is, however, 'DensityMatrix' gives convergent solution for I(V) at V > 1.7V, while 'Off' does not give convergent solution at all at the high voltages !! Is'nt is strange that more reliable method ('Off') does not give a convergent solution, while less reliable ('Densitymatrix') method does.

Can you comment on this observation?

Thanks!

[Anders Blom]

I wouldn't call DensityMatrix less reliable. If you have enough screening, it is the method of choice.

In general, to get convergence above 1.5 V (the exact value depends a lot on the system) is hard, and requires improvements in the algorithms. Such advances have been made in the new DFT code offered as ATK 2009.11, but note that this is not a 100% ready code, it's still being tested and some features are missing. However, during Q1 2010 this will become the full replacement of ATK 2008.10, and should then allow for convergence also at quite high bias - in addition to resolving the constraint issue hopefully once and for all (although it IS a tricky point...).