  When electron-hole pairs are excited in a semiconductor, it is a priori not
clear if they form a fermionic plasma of unbound particles or a bosonic exciton
gas. Usually, the exciton phase is associated with low temperatures. In
atomically thin transition metal dichalcogenide semiconductors, excitons are
particularly important even at room temperature due to strong Coulomb
interaction and a large exciton density of states. Using state-of-the-art
many-body theory including dynamical screening, we show that the
exciton-to-plasma ratio can be efficiently tuned by dielectric substrate
screening as well as charge carrier doping. Moreover, we predict a Mott
transition from the exciton-dominated regime to a fully ionized electron-hole
plasma at excitation densities between $3\times10^{12}$ cm$^{-2}$ and
$1\times10^{13}$ cm$^{-2}$ depending on temperature, carrier doping and
dielectric environment. We propose the observation of these effects by studying
excitonic satellites in photoemission spectroscopy and scanning tunneling
microscopy.
