Self-consistent solution of the Schrödinger-Poisson equations for hydrogen-terminated diamond

A self-consistent one-dimensional solution of the Poisson and Schr\"odinger equations is developed to describe the electronic properties of the hole gas confined below the hydrogen-terminated surface of surface conducting diamond. The energy eigenstates of the confinement potential and the position of the Fermi level are examined as a function of carrier sheet density and temperature. A comparison is made with experimental studies of the hole sheet density for both atmosphere-induced and synthetic surface acceptors. For hole sheet densities below 9×10¹² cm^-2 the Fermi level is within the band gap while for hole sheet densities greater than 9×10¹² cm^-2 the Fermi level resides below the valence-band maximum in the valence band. The dimensionality of the heavy-hole, light-hole, and split-off bands was examined for varying Fermi energy and temperature.