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I have consulted a book by Mark Fox on Optical Properties of Solids, and it states:

" The absorption of a photon by an inter-band transition in a semiconductor or insulator creates an electron in the conduction band and hole in the valence band. The oppositely charged particles are created at the same point in space and can attract each other through their mutual Coulomb interaction... Moreover, if the conditions are satisfied, a bound electron-hole pair can be formed. This neutral bond pair is called an exciton."

My understanding is - We first need to supply E > Eg for excitons to form. Once excitons exist in a material, they facilitate the absorption of photons with E < Eg, specifically at energies corresponding to n=2, n=3 etc. If the material has not been initially supplied with photons of E > Eg, with the material containing no excitons then why do we see an additional absorption response (red lines in figure below) apart from the alpha ~ sqrt(Eg) response we normally observe? I'm confused because I saw spectra such as one below, I don't expect to see absorption below the band gap - we aren't supplying Eg for excitons to form.

I thought that the idea of a spectra is that you provide photons energy from 0 eV to final energy value greater than Eg, starting from low energy and sweep into higher energies.

enter image description here

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  • $\begingroup$ The e-h pair that is created can be either free, or bound. If the bound state is formed, you don't need to create a free pair and have it become bound, it just directly forms the bound state. $\endgroup$ – Jon Custer Oct 13 '20 at 20:27
  • $\begingroup$ Once a bound state e-h pair is formed (I understand that group velocity of electron and hole needs to be the same) then if you again supply energy to this exciton then it would break apart? I read that the position Eg corresponds to where the bound exciton has been ionized to a free e-h pair, and from the graph ^ it would seem that this is correct - the excitons are gone after you supply Eg to them. To me this seems strange that supplying a bound exciton with what seems like an arbitrary energy (Eg) to form the free e-h. Would the exciton not dissociate when binding energy is provided? $\endgroup$ – Aleksejus Pacalovas Oct 13 '20 at 21:43
  • $\begingroup$ Does an absorption spectra at energies of peaks (n = 2, n = 3, ie lower than bandgap energy) simply indicate the formation of bound states ( and hence absorption of photons) or do you need to supply E = Eg for bound states to form? $\endgroup$ – Aleksejus Pacalovas Oct 13 '20 at 21:43
  • $\begingroup$ You can directly form the bound state supplying the appropriate energy that is less than the band gap. $\endgroup$ – Jon Custer Oct 13 '20 at 21:57
  • $\begingroup$ Ok, would I be correct in saying that a bound exciton therefore would exist under the conduction band edge (since we provide the appropriate energy less than the band gap), while on the other hand a free exciton pair would have a hole in the valence band and an electron in the conduction band? $\endgroup$ – Aleksejus Pacalovas Oct 13 '20 at 22:18
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An important thing to keep in mind when talking about excitons is that they are not really hydrogen-like entities formed of real particles, but many-body excitations, i.e. collective behavior of many electrons.

Indeed, the concepts like free electron in a semiconductor, hole and exciton are useful to guide our thinking and often function as good approximations when doing calculations. However, they do not fully reflect the reality: the electrons in a valence band are strongly interacting with each other, and when we speak of a hole we really mean an excitation of this many-particle electron system which, in some respects, behaves as if it were a free particle (with renormalized mass, finite lifetime, etc.) Similarly, a free electron in the conduction band continues to interact with those in the valence band, and is not really a free electron, but also an excitation of this many-body system.

Of course, electrons and holes can be excited only in pairs, and it turns out that some of such pairwise excitations have energies below the gap edge, $E_g$, which is what we call exciton. Such excitations would not exist, if electrons and hole were truly non-interacting particles. However, treating them as a bound state of non-interacting particles produces surprisingly correct predictions, e.g., for their energies.

This idea that in some cases behavior of many-particle system can be represented as that of non-interacting particles is somewhat similar to the concept of Fermi liquid in metals.

A consistent treatment of how the excitons and their hydrogen-like description come about from many-body band structure calculations can be found in the "Theory of Excitons" by Knox.

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