Bias direction for different electrodes

[lohy]

Hi,

I have tried looking through the forum but I couldn't find an answer to my question.
I am investigating the difference between a molecular junction with two Au electrodes and a molecular junction with Au and Al.

Doing so I ran into a definition problem of the forward/reverse current and the chemical potential for the Au-Al junction. It seems that  in this case the Au (left) is kept at 0 and Al(right) is changed.

A forward bias is defined as VL > VR (that being the voltage of the left electrode is higher than of the right)
in the same line the chemical potential is like this: uL < uR.
When I look at the uL given in the transmission spectra (as I understand is the fermi level of the left electrode) at postive 1V I get that uL = 0 and uR = -1.  But this would be uL > uR - so actually reverse bias?

In general I get:
positive 1V: uL=0 , uR = -1
negative 1V: uL=0, uR = +1

I am a little confused here, could you help clarify this for me?

I have attached the note from the tutorial that I tried using to understand this.

Thanks in advance.

[lohy]

Is it that you might have a mistake in the transmission analyzer?

In the transmission spectrum shown in the transmission analyzer, via the iv characteristic, it is written as the fermi level (right) and fermi level (left). Should this instead be the electrode potential? If this is the case the current seems to be correct, if not the current is opposite of what the iv characteristic shows, if you follow the note in my post above.

[Anders Blom]

Short version is that the convention is different for the individual transmission calculations or when you use the IVCharacteristics analysis object. Exactly how this happened is a longer story... You can make IVCharacteristics behave the same way by setting source_electrode=Right, I think (default is left).

[lohy]

Thank you, I can see that when I do as you say it follow the convention.

I am working with a rectifying molecule, so it matters which electrode I choose as the source. So the question is whether I can "trust" the transmissions and IV curve (is the transmission spectrum at e.g. -0.5V correct or is this actually 0.5V) when I use the left electrode as the source when it does not follow the convention? Or can I do something different so it works? 

[Anders Blom]

There is no bug, so you can trust the outcome. It's also impossible for the current to run "backwards", the magnitude may change with many factors, but the direction is only controlled by the bias.

[lohy]

Thank you for your help.

Just to be sure, how should I then understand the fermi levels of the left/right electrode when I have the left electrode as the source (since this does not follow the convention in the tutorials). I cannot find the electrode potentials anywhere only the current and the fermi levels. Is it correct to take the direction of the bias based only on the current I>0 or I<0, and then ignoring the fermi levels? So when I have +0.5V then  VL > VR and I ignore that the fermi levels do not follow this?

[Anders Blom]

It's a bit silly, we should be able to answer this without hesitation... But because of the conflicting conventions plus the option to change the source electrode, maybe you can share a screenshot of what you see in the GUI when you analyze the results, and highlight what is conflicting or unclear in that. It will then be much easier to answer with certainty as it relates to your specific case.

[lohy]

Yes of course. As you can see it is a rectifying molecule I am looking at. The Right electrode is Au and the left is Al. I have no gate (0V) and the transmission is at chosen at -0.5V.  In the transmission spectrum the fermi level of the left electrode is 0 and the right is 0.5.  So as I understand uL < uR indicating that the current should be positive not negative.

I observe a behavior in the transmission changing with the bias that I am investigating together with other properties, so it is important for me to be sure of the direction of the current (and electrons).

As you suggested I tried changing the source electrode to be the right instead of the left electrode. That flipped everything around (more current negative than positive).

So basically I "just" need to be sure of the direction of the current.

It seems that it does not open the bias window up symmetrically, is that also correct? Is this a feature of two different electrodes ? As i recall in the older version it opens up symmetrically, but that could also just be a choice of two Au electrodes…

[lohy]

It actually might just be that it is difficult to undetstand how the bias window opens up.
In the older versions of ATK I understand it opened up symmetrically (so 1V, the bias window would be from -0.5 to 0.5. Is this the same case for the newer versions? (2022 + ) Or is the bias window now from  0V to eg. 1V and -1V to 0V ?

this is not stated anywhere clear in the tutorials. In the transmission where the fermi level of the electrodes are shown it seems like the window is from 0 to -1V (or +1V) depending on the bias. 

[Anders Blom]

Yeah maybe this is the key. In the IVCharacteristics version for computing the transmission, the "source" electrode is set to zero, and the bias applied to the "drain". And with the keyword that we discussed source_electrode you pick which is left/right. Does that help?

Still note that this is all "relative and arbitrary" in the sense that you can always shift an energy scale around, since it has no fixed absolute zero. It is true that for basic TransmissionSpectrum the bias is applied symmetrically, although this is only so because you set a "bias" in the GUI; if you look at the script it will still set the individual electrode voltages, and this can be shifted arbitrarily with no effect on the results as long as the difference remains the same (the bias).

[lohy]

Okay thanks.

Let's say I am looking at the transmission via the IVCharacteristics. The current there is (just to give a number) 1.4*10**-5 at 1V.

To get this current (1.4*10**-5)  at 1V the code would then have the bias window in the transmission spectrum from -0.5 to 0.5 - is the correct?  Or, would the code have the bias window from 0 to  -1V?

I ask about this because I am using the transmissionspectrum to investigate what happens when do an IV sweep - but to do so I need to be sure how the current is integrated from the transmission spectrum.

[Anders Blom]

The current is integrated over the bias window, as it is shown in the transmission analyzer. The same bias can be applied in different ways, but this really just shifts the zero point on the energy axis. The code takes this properly into account.

Note that to be precise, the integral is really done over the entire transmission spectrum range, with the difference of the Fermi functions as weight.

[lohy]

What confuses me a bit when you say that is that when I calculate the current from the transmission spectrums I can only reproduce the IV curve when I have the bias window from -0.5 to 0.5. In the transmission analyzer the left electrode is at 0 and the right is then moved from -1 to 1. So I would assume, based on what you say, that the bias window that is integrated in the code would be e.g. at one point from 0 to 1.  Is this how I should understand it?

[Anders Blom]

No matter how the bias is applied, the current is computed according to the formula in https://docs.quantumatk.com/manual/Types/TransmissionSpectrum/TransmissionSpectrum.html#current. In principle the integral is from -inf to +inf, but in practice of course we can only carry it out for the energy points included in the transmission spectrum calculation.