Atomically thin semiconductors such as monolayer MoS2 and WS2 exhibit
nonlinear exciton-exciton annihilation at notably low excitation densities
(below ~10 excitons/um2 in MoS2). Here, we show that the density threshold at
which annihilation occurs can be tuned by changing the underlying substrate.
When the supporting substrate is changed from SiO2 to Al2O3 or SrTiO3, the rate
constant for second-order exciton-exciton annihilation, k_XX [cm2/s], is
reduced by one or two orders of magnitude, respectively. Using transient
photoluminescence microscopy, we measure the effective room-temperature exciton
diffusion coefficient in chemical-treated MoS2 to be D = 0.06 +/- 0.01 cm2/s,
corresponding to a diffusion length of LD = 350 nm for an exciton lifetime of
{\tau} = 20 ns, which is independent of the substrate. These results, together
with numerical simulations, suggest that the effective exciton-exciton
annihilation radius monotonically decreases with increasing refractive index of
the underlying substrate. Exciton-exciton annihilation limits the overall
efficiency of 2D semiconductor devices operating at high exciton densities; the
ability to tune these interactions via the dielectric environment is an
important step toward more efficient optoelectronic technologies featuring
atomically thin materials