  Two-dimensional materials and their van der Waals heterostructures enable a
large range of applications, including label-free biosensing. Lattice mismatch
and work function difference in the heterostructure material result in strain
and charge transfer, often varying at nanometer scale, that influence device
performance. In this work, a multidimensional optical imaging technique is
developed in order to map sub-diffractional distributions for doping and strain
and understand the role of those for modulation of electronic properties of the
material. As an example, vertical heterostructure comprised of monolayer
graphene and single layer flakes of transition metal dichalcogenide MoS$_2$ is
fabricated and used for biosensing. Herein, an optical label-free detection of
doxorubicin, a common cancer drug, is reported via three independent optical
detection channels (photoluminescence shift, Raman shift and Graphene Enhanced
Raman Scattering). Non-uniform broadening of components of multimodal signal
correlates with the statistical distribution of local optical properties of the
heterostructure. Multidimensional nanoscale imaging allows one to reveal the
physical origin for such a local response and propose the best strategy for
mitigation of materials variability and future device fabrication.
