  Interests in two-dimensional transition-metal dichalcogenides have prompted
some recent efforts to grow ultrathin layers of these materials epitaxially
using molecular-beam epitaxy. However, growths of monolayer and bilayer WSe2,
an important member of the transition-metal dichalcogenides family, by the
molecular-beam epitaxy method remain uncharted probably because of the
difficulty in generating tungsten fluxes from the elemental source. In this
work, we present a scanning tunneling microscopy and spectroscopy study of
molecular-beam epitaxy-grown WSe2 monolayer and bilayer, showing atomically
flat epifilm with no domain boundary defect. This contrasts epitaxial MoSe2
films grown by the same method, where a dense network of the domain boudaries
defects is present. The scanning tunneling spectroscopy measurements of
monolayer and bilayer WSe2 domains of the same sample reveal not only the
bandgap narrowing upon increasing the film thickness from monolayer to bilayer,
but also a band-bending effect across the boundary between monolayer and
bilayer domains. This band-bending appears to be dictated by the edge states at
steps of the bilayer islands. Finally, comparison is made between the scanning
tunneling spectroscopy-measured electronic bandgaps with the exciton emission
energies measured by photoluminescence, and the exciton binding energies in
monolayer and bilayer WSe2/MoSe2 are thus estimated.
