Sharp drop of the mobility of holes with the decrease of their two-dimensional concentration by an external voltage in boron $\delta$-doped diamond layers

By analytical and numerical consideration it is shown that the mobility of holes in boron $\delta$-doped (i.e. with thickness of order several lattice constants) layers in diamond drops with the decrease of their two-dimensional concentration in the process of the $\delta$-doped layer depletion by an external voltage. This drop of the mobility is sharpest for maximal initial hole two-dimensional concentrations of order $\sim$3 $\times$ 10$^{13}$ cm$^{-2}$ (limited from above by the condition of the possibility of their substantial decrease without the electric breakdown of diamond) and is due to the significant mitigation of the screening degree of the ionized boron atom Coulomb potentials and the growth of the efficiency of the scattering of degenerate holes on them owing to the reduction of the kinetic energies of the latter. The corresponding calculations are carried out without the use of the Born approximation (i.e. the perturbation theory) because the conditions of its validity in boron $\delta$-doped layers of diamond are not fulfilled. The predicted effect can be used to increase the source-to-drain current modulation by the gate voltage in diamond field-effect transistors with $\delta$-doped conductive channels.