# Why the optical gap is not identical to the charge gap?

The optical gap is the photon energy required to create an exciton (in a solar cell for example). The charge gap (aka electrical gap) is the energy (voltage) required to create a photon (in an LED for example). Why are these two gaps not identical?

Ref:

Undoped (neutral) conjugated polymers are semiconductors, with optical gaps of ~ 2-3 eV and charge (or band) gaps typically ~ 0.5-1.0 eV higher in energy, reflecting the large exciton binding energies in polymers. (source: Barford, 2013)

• The usual definition of "optical band gap" (at least in the field of photonic crystals which is where I have heard it used most often) is not what you described in your first paragraph, and has nothing to do with photon absorption, electrons, holes, or excitons. – The Photon Aug 6 '15 at 4:47
• Given that, could you share how "optical band gap" or "optical gap" is defined in the text you cited? – The Photon Aug 6 '15 at 4:49
• The reason is given clearly in your reference: the bound excition state is 0.5-1.0 eV below the conduction band edge. – Jon Custer Aug 6 '15 at 16:53
• @JonCuster can you explain that? i.e. how exciton state is related etc. – Sparkler Aug 6 '15 at 17:53
• The existence of exictons makes an asymmetry between absorption (you don't absorb into an exciton state) and emission (you can emit from the excition state). So, no, the two are distinct. – Jon Custer Aug 6 '15 at 19:41

The difference between the fundamental gap (following IUPAC definitions - and your diagram ) (this is what you refer to as your electronic gap in your question) exists because the optical gap corresponds to the energy of the lowest electronic transition accessible via absorption of a single photon. The optical gap is generally substantially lower than the fundamental gap.

The reason for this is that that in the excited state the electron and the hole remain electrostatically bound to one another. This means the magnitude difference between the fundamental gap and the optical gap is related to the binding energy.

The fundamental gap corresponds to the different energy caused due to the sharp bound between eigenvalues in the Schrodinger operator.

So in the diagram you have provided, the fundamental gap is labelled $E_{fund}$, the electron-hole pair binding energy $E_{B}$ is given by $E_{fund}-E_{opt}$.

## Non Technical Summary

The optical gap only lists an electron over the band gap and you must account for the electrostatic effects between your hole and the electron.

The fundamental/electronic gap is the proper quantum energy difference between the energy levels..

The optical or vertical bandgap is the minimum separation between the valence and the conduction band at constant k-value, or electron momentum. The charge bandgap is the separation of the conduction and valence states where these may have different k-values. The optical bandgap is always larger than the charge band gap. Exciton states have an energy somewhat smaller than the optical band gap. The difference is the binding energy, a fraction of the optical band gap.