  Monolayer transition-metal dichalcogenides are direct gap semiconductors with
great promise for optoelectronic devices. Although spatial correlation of
electrons and holes plays a key role, there is little experimental information
on such fundamental properties as exciton binding energies and band gaps. We
report here an experimental determination of exciton excited states and binding
energies for monolayer WS2 and WSe2. We observe peaks in the optical
reflectivity/absorption spectra corresponding to the ground- and excited-state
excitons (1s and 2s states). From these features, we determine lower bounds
free of any model assumptions for the exciton binding energies as E2sA - E1sA
of 0.83 eV and 0.79 eV for WS2 and WSe2, respectively, and for the
corresponding band gaps Eg >= E2sA of 2.90 and 2.53 eV at 4K. Because the
binding energies are large, the true band gap is substantially higher than the
dominant spectral feature commonly observed with photoluminescence. This
information is critical for emerging applications, and provides new insight
into these novel monolayer semiconductors.
