# Why is there a large discrepancy between calculated frequency dependent dielectric function and experimental measurement?

I am calculating the frequency dependent dielectric function of $$\ce{SiC}$$ using VASP. After a geometry optimization, the INCAR file below is used for the calculation. The tags are mostly based on the JARVIS dielectric function database.

AGGAC = 0.0
EDIFF = 1e-07
ENCUT = 520
IBRION = 1
ISIF = 2
ISMEAR = 0
LCHARG = False
LOPTICS = True
LORBIT = 11
LWAVE = False
NBANDS = 600
NEDOS = 5000
NELM = 400
NPAR = 8
PARAM1 = 0.1833333333
PARAM2 = 0.22
PREC = Accurate
LREAL = AUTO
LscaAWARE=.False.


After some post-processing with p4vasp, I can obtain the dielectric function of $$\ce{SiC}$$. Based on my calculations, the real part of the dielectric constant crosses zero around 7.7 eV (that is around 161 nm - I have converted photon energy to wavelength for comparison). This is very similar to $$\ce{SiC}$$ dielectric function available in JARVIS database, so I believe the calculation is consistent.

The problem is that there is a large mismatch between the DFT calculation and the experimental measurement. The experimental data is provided in kim et al. Optica 3, 339-346 (2016). Following is the comparison (first image from my calculation). According the their results the crossover wavelength is in the order of 10 $$\mu$$m. Also note the difference in y-axis magnitudes.

Why is there such a huge difference? Am I doing anything wrong?

## 2 Answers

It's not obvious to me that you are doing anything wrong in your calculation. Your result for the crossover energy seems consistent with the literature, e.g. Theodorou et al. (1999) and Petalas et al. (1998) (the former being a computational work, and the latter a synchrotron experiment). What you should note, however, is that you are using a very different scale to the Kim et al. figure you show, so the comparison you're making is inapplicable. To wit, note that $$12.5~\mu$$m$$=12 500$$ nm $$\gg 160$$ nm. That is, you're plotting UV wavelengths while Kim et al. are considering IR wavelengths. Because of the bandgap in SiC, photons would be expected to couple to electron modes in the UV case, and to phonon modes in the IR case. For a computational approach tackling the latter problem, see Tong et al. (2018).

• Thanks for taking time to answer. In this case, why is phonon resonance missed in the DFT dielectric function? Obviously, I can draw the plot from ~0 eV to about 30 eV. But there is no resonance in $\mu m$ range (< 1 eV). I understand in the final reference you cited, the damping coefficient is found by harmonic/anharmonic IFC calculations to fit a Lorentz model. These require supercells and computationally demanding. Can I assume that phonon resonance is always missed by a DFT calculation? But I find there are some materials having DFT computed dielectric resonance in the IR range. – Achintha Ihalage May 8 at 6:40
• @AchinthaIhalage Probably you didn't compute phonon frequencies? The standard methods were discussed here. Other people on this stack are a lot more familiar with such calculations than myself (I'm not really a DFT person), so don't hesitate to ask a new, more focused question about it. The last reference certainly doesn't represent the only possible way - I picked it since it considered the same SiC polytype as Kim et al., and produced consistent results. – Anyon May 8 at 16:27

Wait, those are two very different resonances. The one at 150-200 nm is obviously of electronic origin, whereas the one at about 12 microns is related to phonon modes. There is quite a lot of experimental data on SiC properties in the infrared, so if you're looking for the experimental data in the uv range, you might want to specify the range in the search. One good way to go about it is to check at https://refractiveindex.info/?shelf=main&book=SiC&page=Larruquert.

• Thanks for the link. It is helpful. As you mentioned 12 microns relates to phonon resonance. But is this not captured by a DFT dielectric function calculation? I find no resonance in micron range. – Achintha Ihalage May 8 at 6:44
• DFT calculations normally consider only electronic degrees of freedom while the nuclei are static. Any resonances from nuclear vibrations/phonons are therefore not captured. A separate calculation is needed to get those. – LukasK May 13 at 13:31