  We study surface charge transfer doping of exfoliated black phosphorus (bP)
flakes by copper using scanning tunneling microscopy (STM) and spectroscopy
(STS) at room temperature. The tunneling spectra reveal a gap in correspondence
of Cu islands, which is attributed to Coulomb blockade phenomena. Moreover,
using line spectroscopic measurements across small copper islands, we exploit
the potential of the local investigation, showing that the n-type doping effect
of copper on bP is short-ranged. These experimental results are substantiated
by first-principles simulations, which quantify the role of cluster size for an
effective n-type doping of bP and explain the Coulomb blockade by an electronic
decoupling of the topmost bP layer from the underlying layers driven by the
copper cluster. Our results provide novel understanding, difficult to retrieve
by transport measurements, of the doping of bP by copper, which appears
promising for the implementation of ultra-sharp p-n junctions in bP.
