I am facing an issue when calculating the dielectric function of Aluminum doped zinc oxide.
I am trying to replicate a paper and the imaginary part of the dielectric function is correct like in the paper I am trying to validate.
However , the real part of the dielectric function at the low energy region (0 to 0.5) should be negative, I am obtaining positive values, it seems that this part is reversed for some reason.
The rest of the real part data is correct.
I am using GGA- PBE- Norm conserving ultrasoft pseudo potentials.
I am really confused as I checked the documentation and it seems that the real part is calculated from the imaginary part, so how come I am getting these reversed values if the imaginary part is correct?
Thank you so much in advance.
The real and the imaginary part of the dielectric function can be calculated from each other using the Kramers-Kronig relations (see e.g. Wikipedia https://en.wikipedia.org/wiki/Kramers-Kronig_relations ). So if you have the correct analytical expression for the imaginary part, but not for the real part, there must be a calculation error in the real part. Or if you have a computer calculated dielectric function there must be a similar software error.
You can use the Kramers-Kronig relations to check the validity of a result.
The error can be in your work, but also in the other paper, of course :-)
Could it be that the program computes the imaginary part of the interband contribution to the dielectric function and then Hilbert transforms it to the real part? The authors of the original paper probably noted that the doping with Al introduces a tiny amount of free carriers into the conduction band and added this contribution, which is negaticve below the plasma frequency an goes to minus infinity at omega=0, by hand. What do you think?
Best, René Monnier
- Badges
- Science topic
- Similar topics
- Correction