What has bandgap gotta do with binding energy and stability?

ByTheCross

Hi,

Could someone clarify the following statement please?

"ZnO has a bandgap of 3.4 eV at room temperature and a free exciton binding energy of 60meV which is much larger than the room temperature thermal excitation energy (25meV) making them stable at rtp."

Does it mean that at rtp, we will not see spontaneous photoemission?

Thanks!

mendes

Why not ? One of the main objectives of studying ZnO is to make for example LED's operating of course at RT !

Also, one of the objectives from research on ZnO is to make a bound exciton based laser since the BE survives as you said even at RT.

Maybe I didn't understand your question.

Cthugha

As I do not know your level of expertise let me start out pretty low. Excitons are basically bound electron-hole complexes and in some sense comparable to the hydrogen atom. The presence of excitons means that there are states at energy slightly smaller than the band gap energy as the Coulomb binding tends to reduce the energy. Optical emission of a direct band gap material can now basically stem from two possible recombination ways: from the electron-hole plasma continuum of unbound electron and hole interband transitions or from exciton recombination. The first offers a continuum of different states/energies while the latter is somewhat more discrete. If you reduce dimensionality (quantum wells, wires or dots), the density of states can indeed become discrete. This exciton recombination is somewhat favourable for applications. However excitons can be ionized again. How much of them will be ionized and how much will exist in a bound state depends on temperature and exciton density. If you are interested, you can calculate it using the Saha equation (which is basically the mass-action law). So at elevated temperatures near room temperature almost all excitons will be ionized for most "showcase" materials like GaAs. However wide bandgap materials like GaN or ZnO allow to have excitons even at room temperature.

However as noted before, spontaneous emission can occur also from ionized carriers. However, as mendes already noted these materials are interesting for applications. Excitons are composite bosons, while unbound ionized carriers are fermions. This means that excitons can in principle undergo bosonic final state stimulation and form a BEC-like state which allows to create spontaneously emitted coherent emission. I think that BEC-like states at room-temperature are interesting goes without saying. So reasonable efforts have been devoted to getting condensates of composite bosons, mostly in terms of polaritons. For ZnO I think the Grundmann group in Leipzig has realized polariton lasing/condensation already.

I suppose this is already more than you asked for. ;)