some question about the voltage profiles

[fan0221]

Helleo everyone,
In the ATk, the bias voltage is defined on the electrodes. Whether or not the voltage profiles are considered as  constant in the electrodes? Is there any difference between the metal electrode and semiconductor electrodes?
Thank you!

[zh]

Helleo everyone,
In the ATk, the bias voltage is defined on the electrodes. Whether or not the voltage profiles are considered as  constant in the electrodes? Is there any difference between the metal electrode and semiconductor electrodes?
Thank you!

The bias voltage applied on the electrodes are considered by shifting rigidly the electrostatic potentials of left and right electrodes, i.e., the applied bias voltage equals to the difference of electrostatic potentials between two electrodes. In the  methodology papers for TranSIESTA, you may find the exact formula or definition for the bias voltage:
Mads Brandbyge, José-Luis Mozos, Pablo Ordejón, Jeremy Taylor, and Kurt Stokbro, Density-functional method for nonequilibrium electron transport, Physical Review B 65, 165401 (2002).
Kurt Stokbro, Jeremy Taylor, Mads Brandbyge, and Pablo Ordejón, TranSIESTA: A Spice for Molecular Electronics, Ann NY Acad Sci 1006, 212-226 (2003).

So, the voltage profile is considered only for the scattering region (i.e., the center region), and there is no difference for the bias voltage applied on the metal electrode and the semiconductor one.

[fan0221]

  Thank you!
In the atk, the voltage profiles are consided as constant in the  metal electrode of central region due to the complete metal screening effect. However, is it still constant in semiconductor electrodes in the ATK?

[Nordland]

In short, yes

The only different between a metallic electrode and semi-conducting electrode is that the metallic electrode has a incomming wave at the fermi energy and a semi-conductor does not.
In all respect they are treated identically.

[fan0221]

  Thank you very much!

[serhan]

Hi,

I've calculated the voltage drop profile of a (6,6) metallic CNT and it is attached to this message. I applied a 0.1V bias voltage and it is clearly seen on the figure. The voltage gradually decreases from 0.1V to zero. It's ok. However, I have a question: In theory, the electron motion is ballistic in these short CNTs, the voltage drop must not occur in the ballistic transport since the scattering is negligible I think. But in the figure, the voltage drops continuously. Is here a conflict? The question is identical to this: There is a fundemamental minimum resistance of (4q^2/h) in a CNT plus an additional resistance caused from scattering effects. Where does this fundamental resistance is? Is it spread along the whole CNT?

Regards,
Serhan

[zh]

Hi,
However, I have a question: In theory, the electron motion is ballistic in these short CNTs, the voltage drop must not occur in the ballistic transport since the scattering is negligible I think.

Please ask yourself a question: Although it's ballistic transport for the electron motion in short CNT, how can the electrons move from one end of CNT to the other end if there is no voltage drop between the ends of CNT? In other words, what is the driving force for the electron motion in CNT at the above situation?  The applied bias voltage on two ends indeed builds up an electric field there,  and the electrostatic potential inside CNT should be continuously from one end to the other end. If no bias voltage applied on two ends of CNT, no voltage drop between two ends of CNT.
 
So what you claimed here is not correct.

But in the figure, the voltage drops continuously. Is here a conflict? The question is identical to this: There is a fundemamental minimum resistance of (4q^2/h) in a CNT plus an additional resistance caused from scattering effects. Where does this fundamental resistance is? Is it spread along the whole CNT?

The conductivity of a conductor is an intrinsic physical quantity, but voltage drop inside conductor is not.  The latter depends on the applied bias voltage. What does contribute to the fundamental resistance or conductivity of a CNT? This is what you or others people are studying now. Maybe, its answer could be found in literature. 

The book entitled "Quantum transport: atom to transistor" by S. Datta, especially in its 1st chapter, explain well the concepts related to your wondering: ballistic transport, conductivity and voltage drop (i.e. potential profile in this book). Kindly recommend you read it to  deeply understand the meaning of "voltage drop".
 

[serhan]

Hi,

Thank you for the answer. However:

In other words, what is the driving force for the electron motion in CNT at the above situation?

Assume a car on a way that is frictionless. Do we need to continuously apply force to move it, or do we give a force (velocity) at the beginning and it continues to move? It is obvious that electron motion is the not the same as a macro car but, the equations are similar in the example.

The conductivity of a conductor is an intrinsic physical quantity, but voltage drop inside conductor is not.

I agree with this statement. The formula I gave is in the first chapter of Datta's book and in his lecture noted as given as movies. The formula (4q^2/h) is the conductance of a ballistic conductor, it is not conductivity, i.e. we do not need to regard the length, diameter, etc. of CNT in order to calculate the net conductance. It is caused from the effort needed to insert an electron into a ballistic channel as I understand from Datta: http://nanohub.org/resources/1831 . Also, this fundamental resistance is modelled as near the contacts of ballistic CNTs in the literature, e.g.: http://ieeexplore.ieee.org/xpls/abs_all.jsp?tp=&arnumber=1159214&isnumber=25976 .

My doubts on this subject remains 

Again thanks for the answer 

Cheers,
Serhan

[zh]

In other words, what is the driving force for the electron motion in CNT at the above situation?

Assume a car on a way that is frictionless. Do we need to continuously apply force to move it, or do we give a force (velocity) at the beginning and it continues to move? It is obvious that electron motion is the not the same as a macro car but, the equations are similar in the example.

If no an initial velocity for a car on an ideal frictionless way (i.e., v=0), how does it move? Obviously, it will always stay there. The driving force mentioned in my previous answer could be understood that this force will give an initial velocity for electron with ballistic motion. Following what you think, it seems that although no bias voltage is applied on the two end of CNT, the current may appear in the CNT.  Indeed, it's impossible to happen.

[Nordland]

Hey Serhan.

From your plot of the voltage drop it appears that you are using the Off constraint in the twoprobe algorithm parameters.
However you get much better result by using the DensityMatrix constaint for calculating the voltage drop.

Oh... forgot to make my main point.

When calculating the voltage drop in ATK, you confine the voltage drop to occur in the scattering region since it is how the boundary conditions are enforced.
For non-perfect/no-periodic systems this is not a problem because the voltage drop would always localize in the area around of junctions, interfaces etc.
However for perfect systems the voltage drop should have an infinite range, since this would minimize the energy, and hence be the ground state of steady flow, and therefore
it becomes an artificial system when we consider voltage drops in perfect systems as we force the system the voltage drop to occur in a very narrow region.
Therefore when we are modeling perfect systems, we never need to perform any non-zero bias calculation unless we want to study the scattering of the artificial potential due to the enforced boundary conditions.

We will simply get the conductivity directly from the transmission spectrum.

Best regards,
   Nordland.

[serhan]

Thank you for your answers. I'll try the DensityMatrix constaint

Cheers
Serhan