Work Function, Photoelectric Threshold, and Surface States of Atomically Clean Silicon

Abstract

The position of the Fermi level at the surface has been determined over the entire available range of bulk dopings for atomically clean (111) silicon surfaces cleaved in a vacuum of ${10}^{\ensuremath{-}10}$ mm Hg. Surface potential is found from the difference in work function and photoelectric threshold. The latter equals the energy difference between the vacuum level and the top of the valance band only for a range of high resistivities where the bands are flat to the surface over the escape depth of emitted electrons (about 25 \AA{}). This photoelectric threshold is 5.15\ifmmode\pm\else\textpm\fi{}0.08 eV. The work function varies only from 4.9 to 4.7 eV in going from extreme $p$ to extreme $n$ type, being close to 4.83 eV throughout most of the doping range. The flat band or neutral surface condition occurs for high-resistivity (\ensuremath{\sim}500 \ensuremath{\Omega}cm) $p$-type bulk doping, for which the Fermi level lies \ensuremath{\sim}0.23 eV below the mid-gap. The results indicate a surface-state density approximately equal to the surface atom density of 8\ifmmode\times\else\texttimes\fi{}${10}^{14}$/${\mathrm{cm}}^{2}$ with the states located in two groups, one normally empty just below the center of the gap and another normally filled just above the valence-band edge.