  To advance fundamental understanding, and ultimate application, of
transition-metal dichalcogenide (TMD) monolayers, it is essential to develop
capabilities for the synthesis of high-quality single-layer samples. Molecular
beam epitaxy (MBE), a leading technique for the fabrication of the
highest-quality epitaxial films of conventional semiconductors has, however,
typically yielded only small grain sizes and sub-optimal morphologies when
applied to the van der Waals growth of monolayer TMDs. Here, we present a
systematic study on the influence of adatom mobility, growth rate, and
metal:chalcogen flux on the growth of NbSe2, VSe2 and TiSe2 using MBE. Through
this, we identify the key drivers and influence of the adatom kinetics that
control the epitaxial growth of TMDs, realising four distinct morphologies of
the as-grown compounds. We use this to determine optimised growth conditions
for the fabrication of high-quality monolayers, ultimately realising the
largest grain sizes of monolayer TMDs that have been achieved to date via MBE
growth.
