  We demonstrate a method to induce tensile and compressive strain into
two-dimensional transition metal dichalcogenide (TMDC) MoS$_{2}$ via the
deposition of stressed thin films to encapsulate exfoliated flakes. With this
technique we can directly engineer MoS$_{2}$ strain magnitude by changing
deposited thin film stress, therefore allowing variable strain to be applied on
a flake-to-flake level. These thin film stressors are analogous to SiN$_{x}$
based stressors implemented in industrial CMOS processes to enhance Si
mobility, suggesting that our concept is highly scalable and may be applied for
large-scale integration of strain engineered TMDC devices. We choose optically
transparent stressors to allow us to probe MoS$_{2}$ strain through Raman
spectroscopy. Combining thickness dependent analyses of Raman peak shifts in
MoS$_{2}$ with atomistic simulations, we can explore layer-by-layer strain
transfer. MoS$_{2}$ on conventional substrates (SiO$_{2}$, MgO) show strain
transfer into the top two layers of multilayer flakes with limited strain
transfer to monolayers due to substrate adhesion. To mitigate this limitation,
we also explore stressors on van der Waals heterostructures constructed of
monolayer (1L) MoS$_{2}$ on hexagonal boron nitride (h-BN). This concept frees
the 1L-MoS$_{2}$ allowing for a 0.85$\%$ strain to be applied to the monolayer
with a corresponding strain induced bandgap change of 75 meV. By using thin
films with higher stress, strain may be engineered to be even higher. Various
stressors and deposition methods are considered, showing a stressor material
independent transfer of strain that only depends on stressor film force with
negligible defects induced into MoS$_{2}$ when thermal evaporation is used.
