Fermi Surfaces of Surface States on Si(111)

Metallic surface states on semiconducting substrates provide an opportunity to study low-dimensional electrons decoupled from the bulk. Angle resolved photoemission is used to determine the Fermi surface, group velocity, and effective mass for surface states on $\mathrm{Si}(111)\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\ensuremath{-}\mathrm{Ag},$ $\mathrm{Si}(111)\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\ensuremath{-}\mathrm{Au},$ and $\mathrm{Si}(111)\sqrt{21}\ifmmode\times\else\texttimes\fi{}\sqrt{21}\ensuremath{-}(\mathrm{Ag}+\mathrm{Au}).$ For $\mathrm{Si}(111)\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\ensuremath{-}\mathrm{Ag}$ the Fermi surface consists of small electron pockets populated by electrons from a few % excess Ag. For $\mathrm{Si}(111)\sqrt{21}\ifmmode\times\else\texttimes\fi{}\sqrt{21}\ensuremath{-}(\mathrm{Ag}+\mathrm{Au})$ the pockets increase their size corresponding to a filling by three electrons per unit cell. The $\sqrt{21}\ifmmode\times\else\texttimes\fi{}\sqrt{21}$ superlattice leads to an intricate surface umklapp pattern and to minigaps of 110 meV, giving an interaction potential of 55 meV for the $\sqrt{21}\ifmmode\times\else\texttimes\fi{}\sqrt{21}$ superlattice.