Electrostatic difference potential and basic parameters

[Arya]

Hi All,

Is electrostatic difference potential same as the conventional 'potential drop'? I know it is the self consistent value obtained from electron difference density using poisson's equation. But I am not able to connect if it same as potential drop and if no how do I see the convention potential drop across a scattering region with respect to its length (z direction) ?

Also, The k point sampling that we set during Huckel Calulation decides sampling of Brillioun zone, right?

What does na, nb in transmission spectrum calculation correspond to?

Thanks,
-Arya

[Anders Blom]

It's not the same as the voltage drop, but if you subtract from it the potential from zero bias, then it is.

You have one set of k-points for expanding the density in Fourier space for the selfconsistent calculation, but there is another set of k-points for the transmission (what you refer to as na and nb) - in this case you usually need more points since the transmission as function of k varies more than the density does.

[Arya]

Thanks Dr Anders !

One more question we have option for No SCF iteration in Huckle model. Now is this the SCF relating to Schrodinger and poisson self consistent solution ? Also in Huckle basis set we have No SCF what does that corresponds to?

Thanks,
-Arya

[Anders Blom]

Yes, SCF or not for the semiempirical models determines whether you include the electrostatic response or not. I didn't understand the point about the basis set...?

[Arya]

Dr Anders,

As you said SCF or not for the semiempirical models determines whether you include the electrostatic response or not. But even if we need to write hamiltonian H=[Kinetic energy +U] we need U which has to be solved self consistently with Poissons equation. Aren't we by default including electrostatics i.e. U and n(electron density)? Without U how else can we write H and calculate n ?

My second question was under 'Huckel Basis Set' we have option for No SCF iteration, what does that corresponds to?

Thanks,
-Arya

[Anders Blom]

The option under Huckel basis set is the same choice as on the main page - for the main control of SCF or Non-SCF. It just appears in two places

Many Huckel models are by definition non-selfconsistent, so you will not include any charge transfer or any response to external fields etc. That's why we have added this to our Huckel (and DFTB etc) models so they can be used for device calculations, etc. But it is required to use the SCF option. For details see either http://quantumwise.com/documents/manuals/latest/ReferenceManual/index.html/chap.atkse.html or K. Stokbro, D.E. Petersen, S. Smidstrup, A. Blom, M. Ipsen, and K. Kaasbjerg, Phys. Rev. B 82, 075420 (2010).

[Arya]

Thanks Dr. Anders,

Couple of more questions,

1. What is periodic boundary conditions? As far as I know it means connecting two distinct end with each other forming a ring like structure? i.e. setting the first(1,N) element in Hamiltonian equal to the last(N,1).

2. The manual says for 'DeviceHuckelCalculator' use poisson solver with MultigridSolver([PeriodicBoundaryCondition,PeriodicBoundaryCondition,DirichletBoundaryCondition]). Now shouldn't it be MultigridSolver([Neumann,Neumann,DirichletBoundaryCondition]). Since the central region is not infinite in a,b direction instead the electric field there is zero.

Thanks,
-Arya

[Anders Blom]

You can choose the boundary conditions as you want and need - the manual entry just describes the default values.

For devices you should of course not have periodic in Z but Dirichlet (or Neumann, as we plan to introduce in ATK 14.2), but it can be periodic in X and Y if there are no gate electrodes. For bulk calculations on the other hand it is customary to have periodic all around because then you can use FFT which is faster, although in principle you could use Neumann for 1D systems.

[Arya]

Thanks Dr. Anders.

The choice of representation in literature is to choose eigenstate representation for x-y direction and real space representation for z direction. With this representation we wont be able to look at electron density/ Electrostatic difference potential in 3D space (correct me if I am wrong).

Can I choose which representation to use in x-y direction?

Thanks,
-Arya


 

[Anders Blom]

If I interpret it correctly, that is just a fancy way of saying that you use an FFT method to solve the Poisson equation in the XY plane, and a real-space multigrid method in Z. That is, just like ATK does. So this is not related to the possibility of extracting the real-space charge density. It does not, however, state the boundary conditions, since you can use the multigrid method both for Neumann, Dirichlet and periodic conditions. Moreover, the periodic case in XY is only valid if there are no gates etc - if you have gates then you need multigrid in all directions, and Neumann/Dirchlet as appropriate.

In ATK you have a full choice for both for the method and the boundary conditions, within the natural limitations of course that FFT can only be used in periodic directions.