  Diamond, a well-known wide-bandgap insulator, becomes a low-temperature
superconductor upon substitutional doping of carbon with boron. However,
limited boron solubility and significant lattice disorder introduced by boron
doping prevent attaining the theoretically-predicted high-temperature
superconductivity. Here we present an alternative co-doping approach, based on
the combination of ionic gating and boron substitution, in hydrogenated thin
films epitaxially grown on (111)- and (110)-oriented single crystals.
Gate-dependent electric transport measurements show that the effect of boron
doping strongly depends on the crystal orientation. In the (111) surface, it
strongly suppresses the charge-carrier mobility and moderately increases the
gate-induced doping, while in the (110) surface it strongly increases the
gate-induced doping with a moderate reduction in mobility. In both cases the
maximum total carrier density remains below $2{\cdot}10^{14}\,$cm$^{-2}$, three
times lower than the value theoretically required for high-temperature
superconductivity. Density-functional theory calculations show that this
strongly orientation-dependent effect is due to the specific energy-dependence
of the density of states in the two surfaces. Our results allow to determine
the band filling and doping-dependence of the hole scattering lifetime in the
two surfaces, showing the occurrence of a frustrated insulator-to-metal
transition in the (110) surface and of a re-entrant insulator-to-metal
transition in the (111) surface.
