  Transition metal dichalcogenides such as MoS$_2$ represent promising
candidates for building blocks of ultra-thin nanophotonic devices. For such
applications, vertically-oriented MoS$_2$ (v-MoS$_2$) nanosheets could be
advantageous as compared to conventional horizontal MoS$_2$ (h-MoS$_2$) given
that their inherent broken symmetry would favor an enhanced nonlinear response.
However, the current lack of a controllable and reproducible fabrication
strategy for v-MoS$_2$ limits the exploration of this potential. Here we
present a systematic study of the growth of v-MoS$_2$ nanosheets based on the
sulfurization of a pre-deposited Mo-metal seed layer. We demonstrate that the
sulfurization process at high temperatures is driven by the diffusion of Sulfur
from the vapor-solid interface to the Mo seed layer. Furthermore, we verify an
enhanced nonlinear response in the resulting v-MoS$_2$ nanostructures as
compared to their horizontal counterparts. Our results represent a stepping
stone towards the fabrication of low-dimensional TMD-based nanostructures for
versatile nonlinear nanophotonic devices.
