  Thin layers of black phosphorus present an ideal combination of a 2D material
with a tunable direct bandgap and high carrier mobility. However the material
suffers from degradation in ambient conditions due to an oxidation reaction
which involves water, oxygen and light. We have measured the spatial profile of
the conductivity on flakes of black phosphorus as a function of time using
scanning microwave impedance microscopy. A microwave excitation (3 GHz) allows
to image a conducting sample even when covered with a dielectric layer. We
observe that on bare black phosphorus, the conductivity changes drastically
over the whole surface within a day. We demonstrate that the degradation
process is slowed down considerably by covering the material with a 10 nm layer
of hafnium oxide. It is stable for more than a week, opening up a route towards
stable black phosphorus devices in which the high dielectric constant of
hafnium oxide can be exploited. Covering black phosphorus with a 15 nm boron
nitride flake changes the degradation process qualitatively, it is dominated by
the edges of the flake indicating a diffusive process and happens on the scale
of days.
