  Single-layer MoS2 is a direct-gap semiconductor whose electronic band
structure strongly depends on the strain applied to its crystal lattice. While
uniaxial strain can be easily applied in a controlled way, e.g., by bending of
a flexible substrate with the atomically thin MoS2 layer on top, experimental
realization of biaxial strain is more challenging. Here, we exploit the large
mismatch between the thermal expansion coefficients of MoS2 and a
silicone-based substrate to apply a controllable biaxial tensile strain by
heating the substrate with a focused laser. The effect of this biaxial strain
is directly observable in optical spectroscopy as a redshift of the MoS2
photoluminescence. We also demonstrate the potential of this method to engineer
more complex strain patterns by employing highly absorptive features on the
substrate to achieve non-uniform heat profiles. By comparison of the observed
redshift to strain-dependent band structure calculations, we estimate the
biaxial strain applied by the silicone-based substrate to be up to 0.2 percent,
corresponding to a band gap modulation of 105 meV per percentage of biaxial
tensile strain.
