Measurements of absolute bandgap deformation-potentials of optically-bright bilayer WSe$_2$

Bilayers of transition-metal dichalcogenides show many exciting features, including long-lived interlayer excitons and wide bandgap tunability using strain. Not many investigations on experimental determinations of deformation potentials relating changes in optoelectronic properties of bilayer WSe$_2$ with the strain are present in the literature. Our experimental study focuses on three widely investigated high-symmetry points, K$_{c}$, K$_{v}$, and Q$_{c}$, where subscript c (v) refers to the conduction (valence) band, in the Brillouin zone of bilayer WSe$_2$. Using local biaxial strains produced by nanoparticle stressors, a theoretical model, and by performing the spatially- and spectrally-resolved photoluminescence measurements, we determine absolute deformation potential of -5.10 $\pm$ 0.24 eV for Q$_{c}$-K$_{v}$ indirect bandgap and -8.50 $\pm$ 0.92 eV for K$_{c}$-K$_{v}$ direct bandgap of bilayer WSe$_2$. We also show that $\approx$0.9% biaxial tensile strain is required to convert an indirect bandgap bilayer WSe$_2$ into a direct bandgap semiconductor. Moreover, we also show that a relatively small amount of localized strain $\approx$0.4% is required to make a bilayer WSe$_2$ as optically bright as an unstrained monolayer WSe$_2$. The bandgap deformation potentials measured here will drive advances in flexible electronics, sensors, and optoelectronic- and quantum photonic- devices through precise strain engineering.