# Optical Band gap determination from absorption coeffecient using DFT

I am currently working with a perovskite material which shows forbidden transitions. Older studies used bigger values of $$\alpha$$ in HSE06 calcualtions(to match with experimental Band Gap) but a recent study showed that this is not the case. Rather the electronic BG is around 0.98 and optical one is around 1.3. This got me thinking how can we differentiate between the two using DFT? I believe the answer should lie in absorption coefficient or the dielectric constant.

In general how can one determine the Optical band gap?

A few possible solutions that I have been thinking about

1. Tauc plot - we could use the absorption coefficient calculated in order to calculate the BG, obviosuly this is motivated from general experimental methodology.
2. Using absorption coefficient - One can look at the critical values of absorption coefficient in order to see where the Optical BG might be. An example is this study.
3. Using imaginary part of dielectric constant - The study in point (2) also says that BG can be determined by looking at the critical BG of imaginary part of dielectric constant but they obtain a different value as compared to Optical BG using (2).
4. Using Penn's model($$\epsilon(0) \approx1+(\hbar\omega_p/E_g)^2$$) one can relate the static dielectric function and the BG. Again (2) as a example.

Furthermore why don't people generally talk about this? Is it because calculation of Optical properties is more computationally costlier than calculation of Electronic ones?

You can calculate the optical gap with TDDFT or GW/BSE. GW/BSE is more common in solids. These are more expensive calculations than DFT calculations, but they are commonly done in metal-halide perovskites.

If I understand that paper correctly, their HSE band gap is smaller than the experimental optical gap. This isn’t necessarily too surprising, since it’s possible that the GW fundamental gap is larger than the HSE fundamental gap, so that excitonic effects would make the optical gap line up with the experimental gap. In some systems, HSE has a comparable fundamental gap as GW, so perhaps this isn’t the case. If you want to compare the fundamental gap to the optical gap, then GW for the fundamental gap and BSE for the optical gap might be your best bet.

They mention a GW0 calculation that had a similarly low band gap; it’s possible that this was underconverged, or that there was some starting point dependence issue that was ran into, or maybe the GW gap actually is close to the HSE gap. This system might be challenging for existing computational methods, so it’s also possible that good agreement with experiment will be tough to achieve.

• Thanks for taking out the time to look into this. But I believe what they are saying is that there HSE calculation results are correct and the electronic BG is truly 0.97 eV. But this is different from Optical BG as there no direct transitions happening between the band edges, the transition rather happens from the middle of the VB to the CB edge. This paper builds upon this idea. Furthermore if you look at fig 7 from original paper they mention "DFT optical gap" which I believe should be coming from some optical spectra.
– Chan
Dec 14, 2022 at 22:09
• Oh yes sorry I missed that the band gap isn’t direct. Their “DFT optical gap” is looking at the direct band gap based on looking at it quickly. Just subtracting DFT eigenvalues can often come close for systems which have small exciting binding energies, but it doesn’t rigorously give you the optical gap.
– AGS
Dec 15, 2022 at 1:23

This is not the actual answer that you asked, but you can get some insight from here. I believe the optical gap is equal to the direct electronic gap at T=0K at a certain k point. Still some more points:

The terms optical vs. eletronic gap are typical when talking about solar cell materials (or the reverse process of electroluminescence). This basically goes back to a distinction between different methods of measuring (or using) the energy gap. When you measure the gap opitcally (e.g. you measure optical absorption as a function of wavelength), you do a kind of excitation spectroscopy: the method doesn't change the charge state of the material, i.e., the number of electrons before and after excitation from valence band to conduction band remains the same. If, however, you measure the position of the bands via electron spectroscopy (e.g. photoemission for the valence band and inverse photoemission for the conduction band, or tunneling spectroscopy to masure both), an extra electron is eihter injected into or taken out of the solid during the process. In order to be able to get that extra electron in, you have to overcome the Coulomb repulsion caused by all the other electrons.

Therefore an electronic gap is usually larger than an optical gap, and the difference is the Coulomb energy for the particular system. In solids with rather delocalized states, this effect may be negligibly small, but in systems with high spatial localization of the valence and conduction states it can be large (especially in organic solar cells or OLEDs).

This efect is not only important for spectroscopy. Also when actually using a device, it makes a difference. In a solar cell, the only important value is the optical gap, because you excite by photons and then separate electrons and holes. In a light-emitting diode, however, applying a bias that correspnds to the optical gap won'tbe enough You have to apply a bias corresponding to the electronic gap, because you first have to inject electrons and holes into the system before they recombine to emit a photon.