# Quantum dot band gap energy equation

I have been looking into certain approximations for band gap energies in quantum dots and I found a paper [1]. However, I noticed that the equations which they obtain are not useful to the situation which I would like to use them in.

What I would like to do is gather information from other articles that show the absorption and emission spectra and understand the size of the quantum dots if the sizes are not given.

I have looked at several papers where $\ce{ZnSe}$ QDs are absorbing and emitting around $\pu{\sim 300 .. 450 nm}$ with sizes from $\pu{2 .. 6 nm}$ in diameter. However, if you use the LDA+C equation for $\ce{ZnSe}$ quantum dots (QDs) ($E_g = 2.54/d^{1.54}$) with diameters of $\pu{\sim 2 nm}$, you get band gaps around $\pu{0.9 eV}$ or $\pu{\sim 1370 nm}$, not $\pu{\sim 400 nm}$ as you would expect.

Is there something I am missing here? Is this a $E_{11}$ transition band gap energy and I am seeing like a $E_{66}$ absorption to $E_{55}$ fluorescence energy emission?

Also, I noticed that there are exciton binding energies which may take up a large portion of the total exciton energy. Are these binding energies important to this problem?

If so, is there a better way to search for and obtain some literature on a simple correlation for these type of energy transitions?

1. Li, J.; Wang, L.-W. Phys. Rev. B 2005, 72 (12), 125325. DOI 10.1103/PhysRevB.72.125325.

I believe the problem was that the LDA+C energies quoted in the paper were extra, additive energies which were supposed to be added to the main band gap energy of the bulk material. In this case that was something like $\pu{2.7 eV}$.