  Hole doping can control the conductivity of diamond either through boron
substitution, or carrier accumulation in a field-effect transistor. In this
work, we combine the two methods to investigate the insulator-to-metal
transition at the surface of nanocrystalline diamond films. The finite boron
doping strongly increases the maximum hole density which can be induced
electrostatically with respect to intrinsic diamond. The ionic gate pushes the
conductivity of the film surface away from the variable-range hopping regime
and into the quantum critical regime. However, the combination of the strong
intrinsic surface disorder due to a non-negligible surface roughness, and the
introduction of extra scattering centers by the ionic gate, prevents the
surface accumulation layer to reach the metallic regime.
