  Band bending is a central concept in solid-state physics that arises from
local variations in charge distribution especially near semiconductor
interfaces and surfaces. Its precision measurement is vital in a variety of
contexts from the optimisation of field effect transistors to the engineering
of qubit devices with enhanced stability and coherence. Existing methods are
surface sensitive and are unable to probe band bending at depth from surface or
bulk charges related to crystal defects. Here we propose an in-situ method for
probing band bending in a semiconductor device by imaging an array of
atomic-sized quantum sensing defects to report on the local electric field. We
implement the concept using the nitrogen-vacancy centre in diamond, and map the
electric field at different depths under various surface terminations. We then
fabricate a two-terminal device based on the conductive two-dimensional hole
gas formed at a hydrogen-terminated diamond surface, and observe an unexpected
spatial modulation of the electric field attributed to a complex interplay
between charge injection and photo-ionisation effects. Our method opens the way
to three-dimensional mapping of band bending in diamond and other
semiconductors hosting suitable quantum sensors, combined with simultaneous
imaging of charge transport in complex operating devices.
