  Recent experimental studies of out-of-plane straining geometries of
transition metal dichalchogenide (TMD) monolayers have demonstrated sufficient
band gap renormalisation for device application such as single photon emitters.
Here, a simple continuum-mechanical plate-theory approach is used to estimate
the topography of TMD monolayers layered atop nanopillar arrays. From such
geometries, the induced conduction band potential and band gap renormalisation
is given, demonstrating a curvature of the potential that is independent of the
height of the deforming nanopillar. Additionally, with a semi-classical WKB
approximation, the expected escape rate of electrons in the strain potential
may be calculated as a function of the height of the deforming nanopillar. This
approach is in accordance with experiment, supporting recent findings
suggesting that increasing nanopillar height decreases the linewidth of the
single photon emitters observed at the tip of the pillar, and predicting the
shift in photon energy with nanopillar height for systems with consistent
topography.
