  Band profiles of electronic devices are of fundamental importance in
determining their properties. A technique that can map the band profile of both
the interior and edges of a device at the nanometer scale is highly demanded.
Conventional scanning tunneling spectroscopy (STS) can map band structure at
the atomic scale, but is limited to the interior of large and conductive
samples. Here we develop a contact-mode STS based on conductive atomic force
microscope that can remove these constraints. With this technique, we map the
band profile of MoS$_2$ transistors with nanometer resolution at room
temperature. A band bending of 0.6 eV within 18 nm of the edges of MoS$_2$ on
insulating substrate is discovered. This technique will be of great use for
both fundamental and applied studies of various electronic devices.
