Fundamental Limits of Exciton-Exciton Annihilation for Light Emission in Transition Metal Dichalcogenide Monolayers

We quantitatively illustrate the fundamental limit that exciton-exciton annihilation (EEA) may impose to the light emission of monolayer transition metal dichalcogenide (TMDC) materials. The EEA in TMDC monolayers shows dependence on the interaction with substrates as its rate increases from 0.1 cm2/s (0.05 cm2/s) to 0.3 cm2/s (0.1 cm2/s) with the substrates removed for WS2 (MoS2) monolayers. It turns to be the major pathway of exciton decay and dominates the luminescence efficiency when the exciton density is beyond 1010 cm-2 in suspended monolayers or 1011 cm-2 in supported monolayers. This sets an upper limit on the density of injected charges in light emission devices for the realization of optimal luminescence efficiency. The strong EEA rate also dictates the pumping threshold for population inversion in the monolayers to be 12-18 MW/cm2 (optically) or 2.5-4x105 A/cm2 (electrically).