Band-bending induced by charged defects and edges of atomically thin transition metal dichalcogenide films

International audience; We report scanning tunneling microscopy/spectroscopy (STM/STS) investigations of the bandbendingin the vicinity of charged point defects and edges of monolayer MoSe$_2$ and mono- andtrilayer WSe$_2$ films deposited on graphitized silicon carbide substrates. By tracing the spatialevolution of the structures of the STS spectra, we evaluate the magnitude and the extent of theband-bending to be equal to few hundreds milielectronvolts and several nanometres, respectively.With the aid of a simple electrostatic model, we show that the spatial variation of the Coulombpotential close to the film edges can be well reproduced by taking into account the metallic screeningby graphene. Additionally, the analysis of our data for trilayer WSe$_2$ provides reasonable estimationsof its dielectric constant ($\epsilon_{WSe}$$_2$ = 20) and of the magnitude of the charge trapped at the defect site(Q = $+e$).