An electron paired with the ‘hole’ it left behind – the empty place, which acts like a positive charge. The two attract each other and form something like a tiny atom. In very thin materials these pairs hold together unusually strongly, so they dominate how the material absorbs and emits light – even at room temperature.
Going deeper
The same electron–hole pair in two settings. In a bulk semiconductor the surrounding crystal screens their attraction, so the pair is large and easily broken. In a monolayer most of the field lines between them pass through the vacuum or substrate around the sheet, where little screens them, so the pair is small and strongly bound.
A hydrogen atom made from an electron and a hole
When light lifts an electron across the , it leaves behind a positively charged hole. The two attract, and if the attraction is strong enough they bind into a neutral pair that moves through the crystal together: an exciton. The physics is that of hydrogen with the proton replaced by the hole – a ground state, a ladder of excited states below the energy of a free , and a characteristic size.
In a conventional the surrounding crystal screens the attraction strongly. An exciton in GaAs spans about 10 nm and is bound by only about 4 meV, well below the thermal energy of about 25 meV at room temperature, so excitons in bulk semiconductors survive mainly in the cold.
Why they are so strong in a single layer
In a the electron and hole are confined to a sheet less than a nanometre thick, and most of the field lines between them run through the vacuum or around it, where there is little to screen them. The attraction is correspondingly stronger and the pair smaller. Monolayer have exciton binding energies of hundreds of meV – about 0.3 eV for WS2 on silicon dioxide – so excitons dominate their optical spectra even at room temperature.
Because screening in a sheet changes with distance, the excited states do not follow hydrogen’s simple 1/n2 ladder; the deviation, a non-hydrogenic Rydberg series, is itself a fingerprint of two-dimensional screening. It also makes the surroundings part of the material: covering the same monolayer with hBN or graphene lowers its binding energy.
A family of excitons
The bright ground state has relatives with entries of their own. are charged excitons that form when extra carriers are present. In tungsten-based TMDCs a -forbidden dark exciton lies below the bright one. And in a the electron and hole can settle in different layers, forming an that lives far longer and can be moved with an electric field.
For specialists
A bound state of a conduction-band electron and a valence-band hole. In 2D semiconductors reduced raises binding energies to hundreds of meV in freestanding TMDC monolayers, so excitons dominate optical spectra at room temperature and follow a non-hydrogenic Rydberg series.