  We exploit scanning probe controlled domain patterning in a ferroelectric top
layer to induce nonvolatile modulation of the conduction characteristic of
monolayer MoS$_2$ between a transistor and a junction state. In the presence of
a domain wall, MoS$_2$ exhibits rectified I-V that is well described by the
thermionic emission model. The induced Schottky barrier height varies from 0.38
eV to 0.57 eV and is tunabe by a SiO$_2$ global back-gate, while the tuning
range of depends sensitively on the conduction band tail trapping states. Our
work points to a new route to achieving programmable functionalities in van der
Waals materials and sheds light on the critical performance limiting factors in
these hybrid systems.
