Hello,
I'm currently working on the formation energy of charged defect with VASP and I'm confused about the energy range that is involved in the equation shown in the figure.
I think an example could be better. In my comprehension, if I have a Fermi energy of 4 eV, an eigenvalue of VBM equal -1 eV and an eigenvalue of CBM equal 0.5 eV, then the energy will goes from 4-1=3 eV to 4+0.5=4.5 eV.
Best regards and thanks for your help
Benjamin Martin
Hello,
(A minor point first - one would usually not speak of charged defects in a system where the Fermi level is outside the bandgap, such a system would be metallic and would screen any concentrated charge imbalance.)
The function of the q(eVBM + Efermi) term is to track the energy cost of "buying" or "selling" electrons from the electron reservoir of the bulk crystal. So if the Fermi level goes up, positively charged defects become harder to form because they must donate the lost electrons into higher energy levels. The Fermi level can be varied within the band gap by doping the semiconductor, which is a process not typically captured in VASP calculations, so rather than giving a single defect formation energy, it is more useful to give it as a function of one variable, Efermi.
Hello,
Thank you for your answer, it sheds light on my understanding of how this term works and therefore the equation.
I'm working on YNiO3 which is a semi-conductor. Its band gap is arround 0.35 eV and in the VASP output files, there are these values:
Fermi energy : 4.34 eV
VBM eigenvalue: -0.11
CBM eigenvalue: 0.22
And I don't know if in the function q(eVBM + Efermi) the (eVBM + Efermi) term goes from -0.11 to 0.22 or if to goes from 4.23 to 4.56. If I understand well "Fermi level can be varied within the band gap" I guess it's the second option.
Something is wrong with the Fermi energy or eigenvalues, the two should be on the same energy scale in VASP and if the Fermi level is above the CBM, it's not the CBM any more. The Fermi level calculation is probably less reliable, can you attach the EIGENVAL file?
You can see from the EIGENVAL file at the first k-point
90 4.009690 4.011482 1.000000 1.000000
91 4.887835 4.888477 0.000000 0.000000
that the VBM must be at least 4.011482 and the CBM must be less than 4.887835 on this energy scale - I haven't checked the rest of the k-points but the VASP-calculated Fermi level is probably within this gap. The method you're using to obtain VBM and CBM has a different energy scale from the eigenvalues - I would guess it is setting the VASP-calculated Fermi level to be zero energy, and defining CBM/VBM relative to that.
I believe the EIGENVAL energy scale would be the appropriate energy scale to use for your formation energy calculations, but you'd have to check that the results made sense.
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