What happens when a free electron meets a hole: the electron drops into the empty state and both are gone. The energy they release leaves either as a photon – radiative recombination, the source of light in LEDs and in photoluminescence – or as heat, usually through a defect that catches one carrier and then the other – non-radiative recombination. How long carriers last before this happens is their lifetime. The share of recombinations that give light decides how brightly a material glows, and in 2D semiconductors defects keep that share small unless they are dealt with.
Large spin–orbit coupling in both bands produces spin-dark and momentum-dark excitons that dominate low-temperature emission, so exciton– phonon coupling and phonon-assisted recombination must be modelled to explain spectra.
An electron in the conduction band and a hole in the valence band are a stored packet of energy, roughly the size of the band gap. When they meet, the electron falls into the hole and the energy has to go somewhere. In radiative recombination it leaves as a photon, which is what a light-emitting diode and photoluminescence rely on. In non-radiative recombination it ends up as lattice vibrations, as heat. The usual route is a defect with a level inside the gap that catches an electron, then a hole – Shockley–Read–Hall recombination; at high densities the energy can instead be handed to a third carrier, Auger recombination.
The lifetime is how long carriers last on average before recombining by any route, and the share that leaves as light is the quantum yield. A material with many defects has a short lifetime and a low yield, however good its band gap.
Excitons in monolayer transition metal dichalcogenides couple to light so strongly that at low temperature they can emit before they have even settled: in MoSe2 at 7 K the intrinsic radiative time is about 1.8 ps, with similar values for WSe2. Warmer, most excitons are kicked by phonons out of the narrow range of momenta that can emit, and the light comes out over a longer time (Robert and colleagues, 2016).
Keeping electron and hole apart slows things down. In MoSe2–WSe2 heterostructures the electron sits in one layer and the hole in the other, and these interlayer excitons live about 1.8 ns – an order of magnitude longer than excitons within one layer (Rivera and colleagues, 2015) – long enough to drift, to be steered by gates and perhaps to condense.
At room temperature most light-generated carriers in an as-made monolayer find a defect first. Exfoliated MoS2 emitted at best about 0.6% of the absorbed light as photons – a sign of many defects. A simple, air-stable treatment with an organic superacid changed that: it removed the defect-mediated non-radiative recombination, raising the quantum yield above 95% and the longest lifetime to 10.8 ns (Amani and colleagues, 2015).
That is why the lifetime and yield of photoluminescence are standard checks of crystal quality, and why passivation, encapsulation and careful growth matter as much for 2D light-emitters and solar cells as the band gap does.
Electron–hole annihilation through radiative (band-to-band or excitonic), Shockley–Read–Hall (trap-assisted) or Auger (energy handed to a third carrier) channels; the measured lifetime follows 1/τ = 1/τ_rad + 1/τ_nr, and the photoluminescence quantum yield is τ/τ_rad. In TMDC monolayers the exciton oscillator strength is so large that the intrinsic radiative time is about 1.8 ps (MoSe2, 7 K), with emission at higher temperature slowed as excitons scatter out of the radiative window. At room temperature defect-mediated non-radiative recombination dominates, holding as-prepared MoS2 to a quantum yield of about 0.6%; an organic superacid treatment removes it, raising the yield above 95% with lifetimes up to 10.8 ns. Interlayer excitons in MoSe2–WSe2 heterostructures, electron and hole in different layers, live about 1.8 ns, an order of magnitude longer than intralayer excitons.
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