  In this letter we report on the synthesis of monolayers of MoS$_2$ via
chemical vapor deposition directly on thin films of Al$_2$O$_3$ grown by
spatial atomic layer deposition. The synthesized monolayers are characterized
by atomic force microscopy as well as confocal Raman and photoluminescence
spectroscopies. Our data reveals that the morphology and properties of the 2D
material differ strongly depending on its position on the substrate. Close to
the material source, we find individual flakes with an edge length of several
hundred microns exhibiting a tensile strain of 0.3%, n-doping on the order of
$n_e=0.2 \cdot 10^{13}$ cm$^{-2}$ and a dominant trion contribution to the
photoluminescence signal. In contrast to this, we identify a mm-sized region
downstream, that is made up from densely packed, small MoS$_2$ crystallites
with an edge length of several microns down to the nanometer regime and a
coverage of more than 70%. This nano-crystalline layer shows a significantly
reduced strain of only <0.02%, photoluminescence emission at an energy of 1.86
eV with a reduced trion contribution, and appears to be p-doped with a carrier
density of $n_h=0.1 \cdot 10^{13}$ cm$^{-2}$. The unusual p-type doping
achieved here in a standard CVD process without substitutional doping,
post-processing, or the use of additional chemicals may prove useful for
applications.
