Experimental Investigation of the Band Structure of Graphite

Abstract

Photoemission and secondary electron emission (SEE) measurements have been used to investigate the band structure of graphite. The energy distribution curves obtained from both types of measurements reveal identical features for those transitions to conduction-band states occurring up to 5 eV above the vacuum level. Two minima in the ${\ensuremath{\sigma}}_{1}$ conduction band, located at critical points ${\ensuremath{\Gamma}}_{3u}^{+}$ and ${Q}_{1u}^{+}$, have been observed at 7.5 and 8.6 eV above the Fermi level. Emission from these final states is observed for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}\ensuremath{\parallel}c$ orientation due to the relaxation of electrons initially excited to ${P}_{3}^{+}$; this $\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}\ensuremath{\parallel}c$ transition, which is observed at 14.5 \ifmmode\pm\else\textpm\fi{} 0.5 eV, is in good agreement with the predicted value of 13.5 eV assigned to transitions ${P}_{3}^{\ensuremath{-}}\ensuremath{\rightarrow}{P}_{3}^{+}$. The $\ensuremath{\sigma}$-band gap at the Brillouin-zone center has been measured for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}\ensuremath{\perp}c$ to be 11.5 \ifmmode\pm\else\textpm\fi{} 0.1 eV and the separation of the $\ensuremath{\sigma}$ bands increases to 15.0 eV at $Q$ in good agreement with the optical reflectivity data. The observation and assignment of interband transitions at higher SEE energies provide additional evidence in support of the two-dimensional band structure proposed by Painter and Ellis. The photoemission measurements give detailed information concerning the nature of the $\ensuremath{\pi}$-band structure at points along the three-dimensional Brillouin-zone face. The splitting of the $\ensuremath{\pi}$ bands at $P$ and $Q$ is observed to be 0.8 eV, which gives rise to $\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}\ensuremath{\perp}c$ transitions at 4.76 and 4.82 eV associated with the saddle-point nature of the $\ensuremath{\pi}$ bands at $Q$, and a value of 0.42 eV for the Slonczewski and Weiss parameter ${\ensuremath{\gamma}}_{1}$. The SEE results locate ${P}_{3}^{\ensuremath{-}}$ below the Fermi level, which provides evidence for electron occupancy at the center of the Brillouin-zone edge in agreement with recent Fermi-surface studies.