Convergence problem at high bias voltage

[pj003]

Hi all,

I got problem of convergence when voltage is applied.
For example, my calculation is ok for 0, 0.2, 0.4 V, but it is not converged at 0.6 V.

Could you please suggest me how to solve this problem?
and why convergence problem happen at higher bias?

Thank you in advance.

[Anders Blom]

Generally speaking, convergence is harder the higher the bias. Some general tips are collected in the newly published tutorial on convergence tricks, I hope these will enable you to proceed!

[Nordland]

Hej pj003.

The reason, why it is harder to converge at higher bias, can often depend on type of system.

When you apply bias, an electric field is introduced into scattering region, and causes a perturbation of the electric field.

I will try to give your some of the reasons of why the system might not converge ( even after the parameters has been tuned )

• Pure metallic system:Since it is very hard to screen perturbations in metallic systesms, and especially if the system is 1D, it can often be hard to get it converge. The best solution is to make the system longer.
• Junctions/Interfaces:If you have a semi-conductor in a sandwich between two metal contacts, and apply a higher bias, the voltage drop is more of less forced to
  be placed across the semi-conductor, this can lead to quite strong perturbation in the semi-conductor. Increase the length of the sandwich layer or be more conservative about the mixing parameters
• Spin-polarized metals: Systems like FeCo, have many different spin-configurations relative close to the fermi energy, hence can a perturbation easy change, the behavior of the system. In this case, I suggest that you either try to to turn the initial scaled spin, or alternative slowly builds up the bias, by restarting from a calculation with slightly less bias. This is in general the best solution always anyway

[tigeryzz]

Hi, Nordland,
you mentioned that as for the pure metallic system, a better way to make it convergence is to make the system longer. Should i make the electrode longer or scattering region longer? And what is the effect of those two way on the convergence?

[Nordland]

It is the scattering region that should be longer.
Once the electrode is longer enough to avoid artificial scattering, then there is no reason for doing more to the electrode and it has not influence of the electrode.

When applying a voltage to a system, a voltage ramp is applied such that the potential increases by the voltage drop across the scattering region. However the effective field strength ( the voltage applied divided by the length of the scattering region ) gives an indication of how strong the system is perturbation this is to the system.
Since it is energetic unfavorable situation and hence the electrons in the system will start to move in order to compensate for the applied field.
However in pure metallic systems that charges has high mobility and hence the electrons moves easily around, and it becomes a tricky issues in terms of convergence to determine the exact location of the compensation charge.

Additional notes:
1) Why does making the system longer help in pure metallic systems? If the system is longer the effective field strength is less, and hence less electrons has to move in order to compensate for the voltage, making the system more stable.
2) If the system is a molecular junction or similar, it is quite easy for the system to determine where the charge should be transfered in order to compensate for the voltage ramp. It will move to the interfaces