Electronic structure of hydrogenated diamond: Microscopical insight into surface conductivity

We have correlated the surface conductivity of hydrogen-terminated diamond to the electronic structure in the Fermi region. Significant density of electronic states (DOS) in proximity of the Fermi edge has been measured by photoelectron spectroscopy (PES) on surfaces exposed to air, corresponding to a $p$-type electric conductive regime, while upon annealing a depletion of the DOS has been achieved, resembling the diamond insulating state. The surface and subsurface electronic structure has been determined, exploiting the different probing depths of PES applied in a photon energy range between 7 and 31 eV. Ab initio density functional calculations including surface charge depletion and band-bending effects favorably compare with electronic states measured by angular-resolved photoelectron spectroscopy. Such states are organized in the energy-momentum space in a twofold structure: one, bulk-derived, band disperses in the $\mathrm{\Gamma }\text{−}X$ direction with an average hole effective mass of $(0.43\pm 0.02)m_0$, where $m_0$ is the bare electron mass; a second flatter band, with an effective mass of $(2.2\pm 0.9)m_0$, proves that a hole gas confined in the topmost layers is responsible for the conductivity of the $(2\times 1)$ hydrogen-terminated diamond $\left(100\right)$ surface.

Figure 1

(a) Angle-integrated PES spectra of the air-exposed (AIR, red squares) and the UHV-annealed (ANN, black squares) HD sample, measured at $h\nu =31$ eV and $h\nu =7$ eV. Black lines are amplified data averages of the ANN sample spectra. A magnification of the Fermi-level region is shown in the inset. (b) LEED pattern of the $(2\times 1)\left(100\right)$ surface after ANN and AIR treatments.

Figure 2

(a) pDOS calculated on a $(4\times 8\times 1) k$-point Monkhorst-Pack grid in the BZ and projected on C atoms at different distances from the surface as a function of energy. pDOS curves, except the bottom one, are offset vertically for clarity. The zero of the energy is the last occupied eigenvalue. Small red spheres mark energy values with same pDOS intensity. (b) Atomic structure of a portion of the supercell, with $\widehat{z}$ axis along the $\left[001\right]$ direction. Gray and white spheres denote C and H atoms, respectively. The position of the ${\mathrm{H}}_{0.75}$ atom is indicated. (c) In-plane averaged local potential $\mathrm{\Delta }V$ (eV) as a function of distance from the surface, $z-z_s$ (nm). The median value of its oscillation in the bulk portion of the supercell ($|z-z_s|\ge 0.7$ nm) is chosen as zero of the $x$ axis. Horizontal arrows link selected pDOS in (a) to corresponding atomic positions in (b) and $z-z_s$ values in (c). (d) pDOS calculated for the ${\mathrm{H}}_{0.75}$ supercell with a uniform grid of $k$ points on the $\mathrm{\Gamma }\text{−}X$ direction. (e) pDOS for a HD supercell without the ${\mathrm{H}}_{0.75}$ substitution on a uniform $k$-point grid along $\mathrm{\Gamma }\text{−}X$.

Figure 3

(a) Spectral weights of theoretical bands unfolded on the $X\text{−}\mathrm{\Gamma }\text{−}X$ direction of diamond p-BZ on a color scale. (b) ARPES band structures along $X\text{−}\mathrm{\Gamma }\text{−}X$ measured on the AIR HD sample at 31-eV photon energy. (c) EDC at ${\mathrm{q}}_{//}=0.3{\AA }^{-1}$.