  The high carrier mobility in graphene promises its utility in electronics
applications. Azobenzene is a widely studied organic molecule for switchable
optoelectronic devices that can be synthesized with a wide variety of ligands
and deposited on graphene. Using first-principles calculations, we investigate
graphene doping by physisorbed azobenzene molecules with various
electron-donating and -accepting ligands. We confirm previous experimental
results that demonstrate greater p-doping of graphene for the trans compared to
cis configuration when using a SO$_3$ electron-accepting ligand, however we
find that NO$_2$ ligands maximize the p-doping difference between isomers. We
also examine how these doping effects change when the graphene monolayer is
supported on a silica substrate. We then extend these findings by examining the
doping effects of an applied electrical bias and mechanical strain to the
graphene, which lead to changes in doping for both the trans and cis isomers.
These results demonstrate a new type of multi-control device combining light,
electric field, and strain to change carrier concentration in graphene.
