Author Topic: ExternalPotential  (Read 1307 times)

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Offline gozde

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ExternalPotential
« on: April 3, 2023, 23:29 »
Hi All, When we dope only the electrodes, why is the same type and amount of compensation charge has added to electrodes and central region as an external potential? Is this necessary to neutralize the system? The second question is, If we want to dope the electrodes with the same type and amount of charge and remain the central region undoped, should this part of the script be as follows?  And the last question, if we change the type or amount of the compensation charge manually which is added to central region as an external potential, how the results are affected, i.e. IVCurve? I'm looking forward to your reply.
Code
# Add external potential
external_potential = AtomicCompensationCharge([
    ('doping_0', 0.01),
    ('doping_1', 0.01)
    ])

left_electrode.setExternalPotential(external_potential)

# Add external potential
external_potential = AtomicCompensationCharge([
    ('doping_0', 0.01),
    ('doping_1', 0.01)
    ])

right_electrode.setExternalPotential(external_potential)

# Add external potential
external_potential = AtomicCompensationCharge([
    ('doping_0', 0.01),
    ('doping_1', 0.01)
    ])

central_region.setExternalPotential(external_potential)

# Add tags
device_configuration.addTags('doping_0', [ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12,
                                          13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23])
device_configuration.addTags('doping_1', [48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
                                          61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71])

Offline Anders Blom

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Re: ExternalPotential
« Reply #1 on: April 4, 2023, 07:27 »
In short, the first part of the central region is really a copy of the electrodes. Strictly speaking, this region only needs to be identical in terms of the positions of the atoms I think, but certainly it will help convergence if the doping also carries over into the central region. In fact, oftentimes it is necessary to have a smooth graduation from high to no doping if you want to have a neutral (undoped) part in the middle.

Offline gozde

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Re: ExternalPotential
« Reply #2 on: April 10, 2023, 12:37 »
Thank you Dr. Blom. As far as I understand, we should not change the charge added by the algorithm to left/right eletrode as well as central region to compensate for the doping. Am I right?

Offline Anders Blom

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Re: ExternalPotential
« Reply #3 on: April 12, 2023, 09:08 »
No, if you compensate, then you remove the doping effect!

Offline gozde

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Re: ExternalPotential
« Reply #4 on: April 14, 2023, 10:36 »
Dr. Blom, sorry to take your time, I think I phrased it wrong. What I mean is that when we dope electrodes, compensation charges are automatically added to the both electrodes and the central region, with the same amount and type of doping by the algorithm. We shouldn't change these compensation charges, right?

Offline Anders Blom

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Re: ExternalPotential
« Reply #5 on: April 17, 2023, 08:02 »
No problem, it's an important and non-trivial question.

It is actually easy to get confused about this way of introducing "doping", because in actual fact we don't dope at all! We could of course, include actual donor or acceptor atoms, like P or As in Si, to achieve a doping effect, but it becomes very difficult to control the concentration in this case, plus the position of the dopant might matter a lot. Therefore, we focus on WHY we dope, the answer being we want to shift the Fermi level closer to the valence or conduction band. But we don't have any control over the Fermi level, it's adjusted self-consistently, thus we need to control it via charge. But, if we just introduce free charge in an NEGF calculation, it will leak out of the system, since there are no net charged cores to retain the electron (as would be case with real dopant P or As atoms). So our only remaining choice is to create "fake" charged atoms, which if we localized the charge to a single atom would be exactly the same as using real dopants. But we can be smart and spread out the charge over several atoms, and thereby control the doing concentration with arbitrary precision. Now, by adding a net positive charge in a region, we actually attract electrons, which are free to float in from the infinite reservoirs (the electrodes), and in this way we achieve n-doping, and opposite for p-doping.

So all this is to say, the doping is an effect of the compensation charges, not the other way around. And therefore, you should not change these charges. Also, it is important to be aware of the amount of compensation charge added, and how this relates to the doping concentration. Since we have a well-defined volume of the electrodes (for 3D cases, at least; it's a bit trickier for 2D), the amount of charged placed on each atom is the desired doping concentration times the volume of the electrode, divided by the number of atoms. If you change this number, you change the doping concentration. This gives a number, the charge per atom, and we can use this both for the atoms in the electrode and those in the central region, for the region of space where we want to have the same doping.

It is essential for good convergence to use the same charges near the central region edges, but If you for instance want the middle of the central region undoped, it can be a good idea to taper these charges towards zero slowly, rather than have a abrupt change to zero at some point. The same technique can be used for a p-n junction, although in practice it seems to work with an abrupt change there, at least for a simple Si p-n case (see our tutorial on this, which notably uses tight-binding; it might work less well with DFT).

I hope this gives a good picture of how we actually use the compensation charges to control doping, and thus your question hopefully answers itself. If not, it is probably better you provide a concrete example and specific system.