About the unit of external potential

[BlackBarrel]

Dear Quantumwise Staff:
    Recently I calculate the external potential and get confused by its unit. Why is it in the unit of eV? Shouldn't it be V?
   
    PS: The manual says "ExternalPotential, returns the electrostatic potential due to the electrodes and gates in the system". How to tell the external potential from the internal one? Is the screening effect included in the external potential calculation?

    Thank you!

[zh]

The unit of a potential  should be eV rather that V.

Please read the background of ATK-DFT to understand the concept of external potential:
http://quantumwise.com/documents/manuals/latest/ReferenceManual/index.html/chap.atkdft.html#sect2.atkdft.kohn_sham_hamiltonian_solving.

[BlackBarrel]

So it is potential energy rather than electric potential? Then is there any way to get the electric potential in voltage induced by the gates? Actually I just want to view the electric field created by gates in my device. May I just divide the external potential (or maybe the difference between the potential of Vg=0 and that of infinite Vg ?) by the electron density?

[zh]

You may follow the concept of voltage drop to extract what you want:
http://quantumwise.com/publications/tutorials/mini-tutorials/98-i-v-curve-and-voltage-drop

[BlackBarrel]

Thank you very much, but the "voltage drop" is still in unit of eV (so why is it called voltage drop?). How could I get the electric field in the device?

BTW, I didn't know the object ElectrostaticDifferencePotential could directly be subtracted from each other. Do all properties' objects support arithmetic operators?

[zh]

Voltage drop (in unit of eV) =  |e| * Voltage drop (in unit of volt).  The electric field induced by the applied bias is calculated by the gradient of voltage drop in the unit of volt: E = -dV/dx.

"Do all properties' objects support arithmetic operators? "
Yes.

[Nordland]

"Do all properties' objects support arithmetic operators? "
Yes.

Yes to all real space properties.

[BlackBarrel]

Voltage drop (in unit of eV) =  |e| * Voltage drop (in unit of volt).  The electric field induced by the applied bias is calculated by the gradient of voltage drop in the unit of volt: E = -dV/dx.

"Do all properties' objects support arithmetic operators? "
Yes.

Many thanks to both of you. So it seems that one can easily divide any potential (external potential, electrostatic difference potential and effective potential) in eV by |e| to get potential in V, regardless of the electron density of the device. Is |e|=1.6E-19 here or |e|=1? Actually what I want to know is the electric field induced by the gates, so is it OK to subtract the external potential of Vg=0 from that of finite Vg?

BTW, what does it mean by real space properties? Is "Transmission Pathways" included? How can I calculate the net current flows into an atom, when there are arrows pointing at it and pointing out from it with similar cylindrical radius? Or at least I want to know the sign of the net current at a certain place to determine the direction of current.

[Anders Blom]

If you consider the definition of the unit "electronvolt", the conversion factor is obvious

All quantities which are expressed on a 3D grid Q(x,y,z) support arithmetic operations. Transmission pathways is thus not included immediately, since it's a discrete function of the pairs of all atoms. But, since ATK uses Python, you can always extract the numbers and perform any operations you want.

The proper quantity to compute for the position-dependence of the current is the current density, although the pathways can in a sense be used to approximate it.

[BlackBarrel]

If you consider the definition of the unit "electronvolt", the conversion factor is obvious

All quantities which are expressed on a 3D grid Q(x,y,z) support arithmetic operations. Transmission pathways is thus not included immediately, since it's a discrete function of the pairs of all atoms. But, since ATK uses Python, you can always extract the numbers and perform any operations you want.

The proper quantity to compute for the position-dependence of the current is the current density, although the pathways can in a sense be used to approximate it.

Thank you, Dr Anders Blom. Well then potential in in unit of eV has its value unchanged if in unit of V, right? What I feel strange is when I calculate the external potential of a device with a gate, the potential at the metallic region (which is about 18eV) doesn't equal what I set in the script (10V) if Neumann boundary condition is employed. There is no such problem with Dirichlet boundary condition. I'm using ATK 12.2. Is it a bug?

Also, the electric field derivated from the external potential is a little parabolic inside the dielectric region. Shouldn't it be linear?

[Anders Blom]

Basically yes, the difference between potential and potential energy is just "e" as in "e"V vs. V. There may be a sign difference though!

There is a bug in the multigrid method for Neumann in 12.2, I'm not sure it would affect the case you mention, it usually manifests itself as a failure of convergence (lots of warning messages in the log file) rather than anything else.

The field is computed fully self-consistently, so there is no inherent reason for it to be linear or any other shape.