nA and nB sampling points' values

[karn]

Hi,

I intend to calculate transmission spectrum and IV curve for a FM-semiconductor-FM structure. I am not sure what values should i assign to nA and nB sampling points in the transmission spectrum analysis box. I have gone through similar Fe/Mgo/Fe tutorial and there they have kept nA=nB=1 and i think it is because it's not a 3D structure while my structure is 3D and that's why nA=nB=1 might not be appropriate for a 3D structure. I reckon in my case nA and nB should be 3 since it's a 3D structure. I will appreciate an expert remark on this. Have a nice day..!!

[Anders Blom]

The FeMgO tutorial uses 30x30, actually, but that's on the low side for that system - for converged results it requires almost 400x400 (for the anti-parallel case).

It's impossible to estimate a priori the sampling needed. You are right that for 1D system you just need 1x1, and for 3D you need more, but to just guess that 3x3 is enough and be happy about it means you are possibly making a very large error. If there are localized spikes in the transmission (in k-space) or for some reason the interesting things happen not at Gamma but perhaps at K, as in graphene, you may need 27x27 instead. Or 100x100. The point is, there is actually no way to know - you simply have to increase the number of points until the results don't change anymore.

[karn]

Thanks for the reply. And one more thing. In fe-mgo-fe tutorial, in calculator nA=6,nB=6,nC=100 and in transmission spectrum nA=30,nB=30. Is there any relation between these two pair of (nA,nB)? Is it possible for them to be completely different from each-other?

[Anders Blom]

There is no relation between these two values. In one case (SCF) it's used to sample the Fourier-space of the electron density, in the other (transmission) of the Green's functions etc. The electron density is rarely a rapidly changing function of k, but the transmission can be.

[karn]

I am not sure if i understand completely...    Yeah, but thanks all the same.

[Anders Blom]

The simple version is, the two k-point samplings do not have to be the same, and in most cases should not be. To figure out the suitable k-point sampling for the self-consistent loop, you should check the convergence of the total energy (for the electrodes, in case of a device). For the transmission, you need to compute the transmission spectrum for 3x3, 9x9, 27x27 or whatever increment you prefer, and check when the current (or transmission spectrum) does not change anymore. Note that at finite bias you may need more k-points than at zero bias.