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 $\mathrm{Si}\mathrm{}\left(111\right)\mathrm{}\sqrt{3}\times \sqrt{3}-\mathrm{Ag},$ $\mathrm{Si}\mathrm{}\left(111\right)\mathrm{}\sqrt{3}\times \sqrt{3}-\mathrm{Au},$ and $\mathrm{Si}\mathrm{}\left(111\right)\mathrm{}\sqrt{21}\times \sqrt{21}-(\mathrm{Ag}+\mathrm{Au}).\mathrm{}$ For $\mathrm{Si}\mathrm{}\left(111\right)\mathrm{}\sqrt{3}\times \sqrt{3}-\mathrm{Ag}$ the Fermi surface consists of small electron pockets populated by electrons from a few % excess Ag. For $\mathrm{Si}\mathrm{}\left(111\right)\mathrm{}\sqrt{21}\times \sqrt{21}-(\mathrm{Ag}+\mathrm{Au})$ the pockets increase their size corresponding to a filling by three electrons per unit cell. The $\sqrt{21}\times \sqrt{21}$ superlattice leads to an intricate surface umklapp pattern and to minigaps of 110 meV, giving an interaction potential of 55 meV for the $\sqrt{21}\times \sqrt{21}$ superlattice.

• Received 3 May 2002

DOI:https://doi.org/10.1103/PhysRevB.66.205302