Fundamental limits of exciton-exciton annihilation for light emission in transition metal dichalcogenide monolayers

Abstract

We quantitatively illustrate the fundamental limit that exciton-exciton annihilation (EEA) may impose on the light emission of monolayer transition metal dichalcogenide (TMDC) materials. The EEA in TMDC monolayers shows a dependence on the interaction with substrates as its rate increases from $0.1\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}/\mathrm{s}$ ($0.05\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}/\mathrm{s}$) to $0.3\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}/\mathrm{s}$ ($0.1\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}/\mathrm{s}$) with the substrates removed for $\mathrm{W}{\mathrm{S}}_{2}$ ($\mathrm{Mo}{\mathrm{S}}_{2}$) monolayers. It turns to be the major pathway of exciton decay and dominates the luminescence efficiency when the exciton density is beyond ${10}^{10}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$ in suspended monolayers or ${10}^{11}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$ 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 $12--18\phantom{\rule{0.16em}{0ex}}\mathrm{MW}/\mathrm{c}{\mathrm{m}}^{2}$ (optically) or $2.5--4\ifmmode\times\else\texttimes\fi{}{10}^{5}\phantom{\rule{0.16em}{0ex}}\mathrm{A}/\mathrm{c}{\mathrm{m}}^{2}$ (electrically).